


NOTES ON 



MECHANICAL DRATTING 



J. r>. PHiLLrps 

H. D. ORTH 



UNIVERSITY OF WISCONSIN 

MADISON 

1912 



JNTOTES 0]sr 

MECHANICAL DRATTING 






J?* DiO^PHILLIPS 
H. r>. ORTH 



UNIVERSITY OF AVISCONSEST 

MAX)IS01Sr 

1912 



Copyright, 1912 

BY 

J. D. PHILLIPS 

H. D. ORTH 



TRACY a KILGORE 

PRINTERS 
MADISON. WIS. 



ir^ 



CCI.A320641 



>M3 / 









CHAPTER 1 



ORTHOGRAPHIC PROJECTION 



^ 1. In Fig. 1 let abc represent the object ABC as it appears 
c2 when viewed through the plane T from the point S. 
^ The figure abc is the projection of the object. 

The plane T is the plane of projection. 

The point S is the point of sig-ht. 

The lines SA, SB and SC are projecting- lines. 

Each point of the object is projected along its projecting line 
to the plane of projection. Thus: — 

The point A is projected along AS to a. 

The point B is projected along BS to b. 

The point C is projected along CS to c. 



r 

iH 2. When the point of sight is at a finite distance fi'om the 

H plane of projection, the representation is called a perspective. 

I^P Fig. 1. In perspective the projecting lines converge from the 

W points of the object to the point of sight. 





Fig. 1 



Fig. 2 



Fig. 3 



When the point of sight is at an infinite distance fi-om the 
plane of projection the projecting lines are parallel. 

If the projecting lines are parallel to each other and oblique 
to the plane of projection, the representation is called an oblique 
projection. Fig. 2. 

If the projecting lines are parallel to each other, and perpen- 
dicular to the plane of projection, the representation is called 
an orthog-raphic projection. Fig. 3. 




Fig. 4 

3. In orthographic projection two or more planes of projec- 
tion are generally used. 

Let Fig, 4 represent a regular triangular prism and its 
projection on the transparent faces of a hollow cube. 

The upper horizontal face of the cube is called the horizon- 
tal plane of projection, or H. 



The front face of the cube is called the vertical plane of 
projection, or V. 

The right side face of the cube is called the rig"ht profile 
plane of projection, or RP. 

The left side face of the cube is called the left profile plane 
of projection, or LP. 

When only one profile plane is used it is designated as P. 
The intersections of these planes kre called ground lines. 
The intersection of H and V is designated as HV. 
The intersection of V and RP is designated as VRP. 
The intersection of V and LP is designated as VLP. 
The intersection of H and RP is designated as HRP. 
The intersection of H and LP is designated as HLP. 
When only one profile plane is used its intersections with H 
and V are designated as HP and VP, respectively. 

4. Each point of the object is viewed in a direction perpen- 
dicular to each of the planes of projection. Thus, A" repre- 
sents the point A as it appears when viewed from above in a 
direction perpendicular to H. A^ represents the point as it ap- 
pears when viewed from in front in a direction perpendicular to 
V. A*^^ represents the point as it appears when viewed from the 
right in a direction perpendicular to RP, and A^^ represents the 
point as it appears when viewed from the left in a direction per- 
pendicular to LP. 

5. The projection of the object on the horizontal plane is 
called the top view, plan, or horizontal projection. That on 
the vertical plane is called the front view, front elevation, 
or vertical projection. The projections on the right and left 
profile planes are called the rigrht and left side or end views, 
rig-htand left side elevations, or right and left profile pro- 
jections. The bottom and rear views of an object are seldom 
necessary. The expressions top view, front view, right side 
view and left side view are preferred. The terms plan, front 
elevation, side elevation are used in architectural work. In 
treatises on descriptive geometry the terms horizontal projection, 
vertical projection and profile projection are employed. 





A^" 


Q. 

_) 
> 


^— 




A"'' 










a 

> 

R 








LEFT SIDE 


FRONT 


I6HT SIDE 





Fig. 5 





• 










ir 

X 


- 








CL 

-J 

r 






a" 




a"" 






LEFT SIDE 






TOP 






Right side 





Fig. 6 











, 








a" 










1 
TOP 








A^" 




1 

1 ,/ 
|A^ 






a"^ 








CL 

_l 
> 


/\ 


VRP 








LEFT SIDE 




FRONT 


RIGHT 5IDE 



Fig. 7 



6. The projecting lines AA" and AA^ , Fig. 4, determine a 
plane perpendicular to HV. 

The projecting lines AA^ and AA"^^ or AA^'' determine a plane 
perpendicular to VRP and VLP. 

The projecting line AA" and AA^^ or AA''^ determine a plane 
perpendicular to HRP and HLP. 

Hence: — A point and its projections on any two of the planes 
of projection will determine a plane perpendicular to the inter- 
section of those planes. 

7. In order to represent the object on a single plane, as a 
sheet of drawing paper, the planes of projection are revolved 
into H or V. 

8. (rt) When the front and side views are required the profile 
planes are folded into V. Fig. 5. 

(6) When the top and side views are required the profile 
planes are folded into H. Fig. 6. 

(c) When the top, front and side views ai-e required the pro- 
file planes are revolved into V. Fig. 7. 

9. When the profile planes are revolved into the vertical 
plane the profile projections of any point will remain in a plane 
perpendicular to VRP or VLP. Thus, A''^ Figure 4, will take 
the position A*^"", Fig. 5, on a horizontal line through A^ . 

When the profile planes are revolved into the horizontal plane 
the profile projections of any point will remain in a plane per- 
pendicular to HRP or HLP. Thus, A''^ Fig. 4, will take the 
position A'^'', Fig. 6, on a horizontal line through A". 

When H and V are revolved into one plane A" and A^ will 
lie in the same perpendicular to HV. 

10. Points in space are designated by capital letters A, B, C, 
etc.; the corresponding horizontal projections by A", B", C", 
etc-; and the corresponding vertical projections by A\ B\ C\ 
etc. 

11. Solids are limited by surfaces. 
Surfaces are limited by lines (edges) . 
Lines are limited by points (corners). 



The projections of a solid will contain the corresponding pro- 
jections of its limiting surfaces, lines and points. 

12. Let Fig. 8 represent a triangular prism and its projec- 
tions on H and V. 

The face ABC, Fig. 8, is parallel to V, and therefore per- 
pendicular to H. 

(a) Its front view, Figs. 8-9-10. is the same form and size 
as the face of the prism. 



/ 


/ 


/ / 


/ 


/HV 


r~ 


1 


1 


i 


^ 

" 


1 ^^ 


1 

1 




N 


^/B 




V 







B" 








c" 

HV 


lA" 

1 
1 




1 
1 

A 


^ 


C 





c" 




Fig. 



Fig. 9 



Fig. 10 



(6) Its top view. Figs. 8-9-10, is a straight line parallel to 
HV. 

Hence, if a plane figure is parallel to V its front view will be 
a figure of the same form and size as the figure in space, and its 
top view will be a straight line parallel to HV. 

Likewise, if a plane figui-e is parallel to H, its top view will 
be a figure of the same form and size as the figure in space, and 
its front view will be a straight line parallel to HV. 

13. Let Fig. 11 represent a triangular pyramid and its pro- 
jections on H and V. 



The face ABFE, Fig. 11, is perpendicular to V and inclined 
to H and P. 

(a) Its front view, Figs. 12-13, is a straight line. This line 
mates a angle with HV equal to the angle the face in space 
makes with H. 

(6) Its top view, Figs. 12-13, is a figure which is less than 
the true size of the face in space. 



14. Let Fig. 14 represent a regular triangular prism and its 
H and V projections. 

The edge AE, Fig. 14, is perpendicular to V and therefore 
parallel to H. 

(a) Its front view, Figs. 15-16, is a point. 

(&) Its top view, Figs- 15-16, is a straight line perpendicular 
to HV and equal in length to AE. 








e" 


r" 






a" 


b" 


HV 




A 


., 


B 



Fig. 11 



Fig. 12 



a" b 







e" 












riv 


1 






1a' 












Fig. 13 



Fig. 14 



Fig. 15 



Fig. 16 



Hence, — If a plane figure is perpendicular to V and inclined 
to H, its front view will be a straight line which will make an 
angle with HV equal to the angle the figure in space makes 
with H. 

The top view will be less than the true size of the figure in 
space. 

Likewise, if a plane figure is perpendicular to H and inclined 
to V its top view will be a straight line which will make an 
angle with HV equal to the angle the figure in space makes with 
V. The front view will be less than the true size of the figure 
in space. 



Hence. — If a straight line is perpendicular to V its front view 
is a point and its top view is a straight line perpendicular to 
HV and equal in length to the line in space. 

Likewise, if a straight line is perpendicular to H, its top view 
is a point and its front view is a straight line perpendicluar to 
HV and equal in length to the line in space. 

15. Let Fig. 17 represent a regular triangular prism and its 
H and V projections. 

The edge BC, Fig. 17, is parallel to H and V. 

(a) Its top and front views. Fig. 17-18-19, are parallel to HV 
and equal in length to the line in space. 



Hence,— If a straight line is parallel to H and V its H 
and V projections are parallel to HV and equal in length to the 
line in space. 

16. Let Fig. 20 represent a regular triangular prism and its 
H and V projections. 

The edge AC, Fig. 20, is parallel to V and inclined to H 
and P. 


















HV 




B" 




A 




c 




B' 



Fig. 17 



Fig. 18 




make an angle with HV equal to the angle the line in space 
makes with V. The front view will be parallel to HV and 
shorter than the true length of the line. 



/ / / 



/h\j 


1 


1 


i 


1 

i 




h 


\ 




V 



Fig. 20 









HV 








1^" 

1 






1 
1a' 

A 




c 







Fig. 21 



C" A" 




Fig. 22 



Fig. 19 



(a) Its front view, Figs. 21-22, is a straight line equal in 
length to AC. This view makes an angle with HV equal to the 
angle AC makes with H. 

(fe) Its top view. Figs. 21-22, is a straight line parallel to HV 
and shorter than the true length of the line. 

Hence, — If a straight line is parallel to V and inclined to H, 
its front view will show the true length, and will make an angle 
with HV equal to the angle the line in space makes with H. The 
top view will be parallel to HV and shorter than the true length 
of the line. 

Likewise, if a straight line is parallel to H and inclined to V 
its top view will be equal to the true length of the line, and will 





Fig. 23 



B" 



PROBLEMS 

17. To draw the top and and front view of a regular square 
prisna having its base parallel to H and two of its lateral faces 
parallel to V. Fig. 23. 

Since the bases of the prism are par- 
allel to H: 

(a) Their top view A"B"C"D", Fig. 
24, is the same form and size as the 
bases in space. 

{&) Their front views A'D'' and F'E'', 
Fig. 24, are straight lines parallel to 
HV. 

Since two of the lateral faces are par- 
allel to V: 

(a) Their front view A'D'E'F'', Fig. 
24, is the same form and size as the faces 
in space. 

(6) Their top views A^D^ and B^C^ 
are straight lines parallel to HV. 

1. Draw top and right side views of a 
regular square prism. Bases parallel to 
H. Two opposite lateral faces perpen- 
dicular to P. 

2. Draw the front and left side views 
of a regular square prism. Bases par- 
allel to V. Two opposite lateral faces 
parallel to P. 

3. Draw the front and right side views 
of a regular square prism. Bases par- 
allel to P. Two opposite lateral faces 
parallel to V. 

4. Draw the left side and top views of 
Bases parallel to P. Two opposite lat- 



TOP 



FRONT 

Fig. 24 



a regular square prism, 
eral faces parallel to H. 

1 8. To draw the front and right side views of a regular hexa- 



gonal prism having its bases parallel to P and two of its lateral 
faces perpendicular to V. Fig. 25. 



FRONT 




Fig. 26 



Fig. 25 



Since the bases are parallel to P : 

(a) Their side view, Fig. 26, is a regular hexagon of the same- 
form and size as the bases in space. 

(6) Their front views, Fig. 26, are straight lines parallel to- 
VP. 

Since two of the lateral faces are perpendicular to V: 

(a) Their front and side views. Fig. 26, are straight lines 
perpendicular to VP. 

1. Draw the front and end views of a regular hexagonal 
psism. Bases parallel to P. Two opposite lateral faces parallel 
to V. 

2. Draw the top and end views of a regular hexagonal prism. 
Bases parallel to P. Two opposite lateral faces parallel to H. 

3 Draw the top and front views of a regular hexagonal 
prism. Bases parallel to H. Two opposite lateral faces parallel 
to V. 

4. Draw the front and right side views of a regular hexagonal 
prism. Bases parallel to V. Two opposite lateral faces perpen- 
dicular to P. 

19. To di-aw the top and front views of a right circular cylin- 
der. Fig. 27. 

Since the bases are parallel to H : 



(rt) Their top view, Fig. 28, is a circle of tlie same size as the 
bases of the cylinder. 

(6) Their front views, Fig. 28 are straight lines parallel to 
HV. 

In viewing the cylinder through the vertical plane, one-half 
of the curved surface is seen and the other half is hidden. The 
elements which separate the visible from the invisible portions 
of the surface are called extreme elements of the cylinder. 

1. Draw the front and right side views of a right circular 
cylinder. Bases parallel to P. 

2. Draw the top and front views of a right circular cylinder. 
Bases parallel to H. 

3. Draw the front and left side views of a right circular cylin- 
der. Bases parallel to V. 

4. Draw the front and right side views of a right circular cyl- 
inder. Bases parallel to V. 

20. To draw the top and front views of a regular square 
prism having its bases parallel to H and two of its lateral faces 
at an angle of 30° to V. Fig. 29. 

Since the bases are parallel to H: 

(a) Their top view, Fig. 30, is the same form and size as the 
bases in space. 

(b) Their front views, Fig. 30, are straight lines parallel to 
HV. 

Since two of the lateral faces make an angle of 30° to V: 

(a) Their top views, Fig. 30, are straight lines making an 
angle of 30° to HV. 

{b) Their front views, Fig. 30, are less than the true size of 
the face in space. 

The edge which is not seen in the front view is shown by a 
dotted line. 

1. Draw the top and front views of a regular square prism. 
Bases parallel to V. Two opposite lateral faces 30° to H. 

2. Di-aw the front and right end views of a regular square 
prism. Bases parallel to P. Two opposite lateral faces 60° 
with V. 



3. Draw the left and front end views of a regular square 
prism. Bases parallel to P. Two opposite lateral faces 30° 
with V. 

4. Draw the front and right side views of a regular square 
prism. Bases parallel to V. Two opposite lateral faces 60° to P. 




Fig. 27 




TOP 



FRONT 

Fig. 28 




Fig. 29 




TOP 



FRONT 

Fig. 30 




21. To draw the top and front views of a regular square pyra- 
mid having its base parallel to H and two of the edges of its 
base parallel to V. Fig. 31. 

Since the base is parallel to H: 

(a) Its top view, Fig. 32, is a square of the same form and 
size as the base of the pyramid. 

(b) Its front view, Fig. 32, is a straight line. 
Since the two edges of the base are parallel to V: 

(a) Their top and front views. Fig. 32, are straight lines par- 
allel to HV. 

Since the altitude of the pyramid is parallel to V: 

(a) Its top view is a point. 

(&) Its front view is a straight line parallel to HV. 

1. Draw the top and front views of a regular square pyramid. 
Base parallel to V. Two opposite edges of the base parallel to H. 

2. Draw the front and right side views of a regular square 
pyramid. Base parallel to V. Two opposite edges of the base 
parallel to P. 

3. Draw the front and left side views of a regular square pyra- 
mid. Base parallel to V. Two opposite edges of the base par- 
allel to P. 

4. Draw the front and right side views of a regular square 
pyramid. Base parallel to P- Two opposite edges of the base 
parallel to V. 

22. To draw the top and front views of a regular square 
pyramid having its base parallel to H and two of the edges of its 
base at an angle of 30° to V. Fig. 33. 

Since the base is parallel to H: 

(«) Its top view, Fig, 34, is a square of the same form and 
size as the base of the pyramid. 

{!)) Its front view. Fig. 34, is a straight line parallel to HP. 

Since two of the edges of the base are parallel to H and 30° 
to V: 

(a) Their top views, Fig. 34, are straight lines making an 
angle of 30° to HV. 

(6) Their front view, Fig. 34 is a straight line parallel to HV. 



1. Draw the top and front views of a regular square pyramid. 
Base parallel to V. Two opposite edges of the base 30° to H. 

2. Draw the front and right side views of a regular square 
pyramid. Base parallel to V. Two opposite edges of the base 
30° to P. 

3. Draw the front and leftside views of a regular square pyra- 
mid. Base parallel to V. Two opposite edges of the base 60° 
to P. 




Fig. 31 




Fig. 33 





FRONT 

Fig. 32 



FRONT 

Fig. 34 



10 



4. Draw the front and right side views of a regular square 
pyramid. Base parallel to P. Two opposite edges of the base 
30° to V. 

23. To draw the top and front views of a right circular cone 
having its base parallel to H. Fig. 35. 

Since the base is parallel to H: 

(a) Its top view, Fig. 36, is a circle of the same form and 
size as the base of the cone. 

(b) Its front view, Fig. 36, is a straight line parallel to HV 
and equal in length to the diameter of the base. 

In the front view one-half of the curved surface is seen. The 
two elements which separate the visible from the invisible por- 
tion are called the extreme elements of the cone. 

1. Draw the top and front view of a right circular cone. Base 
parallel to V. 

2. Draw the front and right side views of a right circular 
cone. Base parallel to V. 

3. Draw the front and left side views of a right circular cone. 
Base parallel to V. 

4. Draw the front and right side views of a right circular cone. 
Base parallel to P. 

24. To draw the top and front views of a sphere. Fig. 37. 
A sphere is represented by its contours. These contours are the 
great circles of the sphere which are parallel to the planes of 
projection. Since the top and front views are required the great 
circles which represent the sphere will be parallel to H and V 
repsectively. Fig. 38. 





Fig. 35 



Fig. 37 





TOP 



TOP 





FRONT. 

Fig. 36 



FRONT 
FrG. 38 



11 



THE THIRD PLANE 

25. When more than the vertical and horizontal projections 
of an object are necessary, or when either of these projections 
with a third view is required to completely represent the object 
a third plane of projection is used. 

The third plane of projection ordinarily used is perpendicular 
to both H and V and is called a profile plane or P. 

When an object is to be represented on the H, V and P planes 
each of its points will be viewed in three directions namely per- 
pendicular to H, perpendicular to V and perpendicular to P. 




Fig. 39 



Fig. 40 



It is sometimes necessary to draw inclined views of an object 
situated in a simple position, or the H and V views of an object 
placed in an inclined position. In such cases planes of projec- 
tion inclined to one of the principal planes of projection and 
perpendicular to the other are used. These are called auxiliary 
planes of projection, or Q. 

When an auxiliary plane is perpendicular to H its intersection 
with H is designated as HQ. Fig. 39. In this ease lines per- 
pendicular to H are parallel to V and Q. Such lines will there- 
fore be projected perpendicular to HV and HQ, respectively. 
Fig. 40. Hence, dimensions perpendicular to HV are equal to 
dimensions perpendicular to HQ. 



OF PROJECTION 

When an auxiliary plane is perpendicular to V its intersection 
with V is designated as VQ. Pig. 41. In this case lines per- 
pendicular to V are parallel to H and Q. Pig. 42. Such lines 
will be projected perpendicular to HV and VQ respectively. 
Hence, dimensions perpendicular to HV are equal to dimensions 
pei-pendicular to VQ. 

26. To draw the top, front and side views of a regular hexa- 
gonal prism having its bases parallel to P and two of its lateral 
faces parallel toH. Fig. 43. 





Fig. 41 



Fig. 42 



Since the bases are parallel to P: 

(a) Their side view. Fig. 44, is a regular hexagon of the same' 
form and size as the bases of the prism. 

(b) Their front and top views. Fig. 44, are straight lines par- 
allel to VP and HP respectively. 

Since two of the lateral faces are parallel to H: 

(a) Their top view. Fig. 44, is a rectangle of the same form 
and size as the lateral faces of the prism. 

(&) Their front and end views, Fig. 44, are straight lines per- 
pendicular to VP. 

The vertical dimensions on the top view are equal to the 
hoi'izontal dimensions on the side view. 

1. Draw the top, front and left side views of a regular hexa- 



I 



12 



^^ 



gonal prism. Bases parallel to P. Two opposite lateral faces of 
the prism parallel to V. 

2. Draw the top, front and right side views of a regular hexa- 
gonal prism. Bases parallel to V. Two opposite lateral faces 
parallel to H. 

3- Draw the top, fi-ont and left side views of a regular hexa- 
gonal prism. Bases parallel to H. Two opposite lateral faces 
parallel to P. 



VQ, and makes an angle with HV equal to the angle Q makes 
with H. 

(c) Their top views are ellipses. Chords of the upper base 
which are perpendicular to HV in the auxiliary view are pro- 
jected on H in their true lengths. Thus, A^B" =A«B*5. E^ 
F^ = E'^F^, etc. Points on the top view of the lower base may 
be found in the same manner. 



TOP 



FRONT 



Fig. 44 




FRONT 



Fig. 43 



Fig. 46 



Fig. 45 



27. To draw the top, front and auxiliary views of a right cir- 
cular cylinder having its bases parallel to an auxiliary plane. 
Fig. 45. 

Since the bases are parallel to Q: 

(a) Their auxiliary view. Fig. 46, is a circle equal in size to 
the bases of the cylinder. 

(6) Their front view, Fig. 46, is a straight line equal in 
length to the diameter of the cylinder. This view is parallel to 



28. To draw the top, front and auxiliary views of a right 
circular cone having its base parallel to an auxiliary plane Q, 
which is perpendicular to H and inclined to V. Fig. 47. 

Since the base is parallel to Q : 

(a) Its auxiliary view. Fig. 48, is a circle of the same form 
and size as the base of the cone. 

(6) Its top view is a straight line equal to the diameter of the 
base. This view is parallel to HQ and makes an angle with HV 
equal to the angle Q makes with V. 



13 




(c) Its front view is an ellipse- 

The major axis of the ellipse is the front view of the diameter 
of the base which is perpendicular to H. C^ is its top view and 
C^D"^ is its front view. The minor axis of the ellipse is the 
front view of the diameter of the base which is parallel to H. 
j;;hjih ^^^^ gvpv g^j.g |^g ^^p ^^(j front views respectively. Since 

the chord AB is perpendicular to H its front view A'^B'^ is equal 
to A'^B'^. The front view of the vertex is on the minor axis 
produced. The extreme elements in the front view are tan.^ent 
to the ellipse. Thej' do not meet the major axis at its extrem- 
ities. 



Fig. 47 



SECTIONS AND DEVELOPMENTS 



29. When an object is cut by an imaginary plane and a portion 
on either side of the plane is removed, the surface exposed is 
called a section. 

If the object is viewed in a direction perpendicular to the sec- 
tion plane and the porl!ion of the object beyond the section plane 
is shown, the view is called a sectional view. 

Tiie section of an object is found by finding the points in 
which its elements OF edg-es pierce the given section plane. 
Thus in Fig. 49 the edges of the prism pierce the section plane 
in points which when joined determine the form of the section. 

30. If a surface of a solid is rolled into a plane called the 
plane of development, the portion of the plane touched by the 
surface will be equal to the given surface and is the develop- 
ment of the surface. The development may be started by 
placing any straight line element in contact with the plane of 



development. The edges of the base of a right prism will roll 
out into a straight line perpendicular to the lateral edges. The 
development of a surface may be rolled into the original form of 
the surface. Double curved surfaces such as a sphere are not 
developable. 

31. To find the section of a regular square prism, cut by a 
plane perpendicular to V and inclined to H and P. Show the 
true size of the section and develop the lateral surface of the 
prism. 

Let Fig. 49 represent the top, front and right side views of 
the prism; QQ is the front view of the given section plane. 

Find the points in which the edges of the prism pierce 
the section plane. 

These piercing points are first located in the front view, since 
this view of the section plane is a straight line. 



14 



The top and side views of the piercing points are projected 
to the top and side views of the corresponding edges, thus: — 

The edge BF pierces the plane QQ'at point 0, which is pi"o- 
jected at O'^ in the front view, at 0^ in the top view and at 0^ 
in the side view. 




Fig. 49 

Straight lines joining the piercing points NOPLMN in order, 
form the outline of the section. 

Since QQ is not parallel to either of the planes of projection 
the true size of the section is not shown. In order to construct 
the true size of the section, I'ectangle WXYZ is drawn in QQ 
enclosing the section figure. WX and YZ are parallel to H and 
P and therefore show in their true lengths on H and P. XY and 



WZ are parallel to V and therefore show in their true lengths 
on V. In constructing the true size of WXYZ and locating 
the corners of the section in its sides, true lengths along each 
line are obtained from the view in which the line shows in its 
true length. 

Lay off (XY)Q = (XY)^ and (XW)'^ = (XW)h perpendicular 
to (XY'.^. Complete the rectangle. 

On(XY)Q lay off (X0)« = (XO)^. Locate L'^ in the same 
manner. 

On (XW)«lay off (XM)«=(XM)h. Locate N« and P<J in the 
same manner. 




Lines joining points (NOPLMN)*^ in order, form the true out- 
line of the section. 

In the development of the lateral surface of the prism. Fig. 
50, the base rolls out into a straight line (GGi )". 

(GH)'* (HE)« (EF)« and (FGi)« are each equal to the corre- 
sponding side of the base, the true length of which is seen in 
the top view. 

Lay off (GO)"* = (GC)'^, the true length of the edge, perpen- 
dicular to (GGi)''. The completed rectangle (GCCiGi)'* is the 
development of the lateral surface of the prism. 



15 



To find tlie outline of the section in the development lay off 
(GP)«= (GP)^. Locate Lf, O^, and Pi« in like manner. 

Lay off (AN)« equal to (AN)^ and (MA)» equal to (MA)^ . 

Straight lines joining (PLMANOPi)^ in order, show the 
outline of the section. 

32. To find the section of a right circular cylinder cut by a 







x' 




b; 


w 




N'[ 




g 


Wi 




M 




^^ 






■//^ 


y////^/ 


yZv// 






H'l 


^P 


A' 


G' 



Fig. 51 

plane perpendicular to H and inclined to V and P. Show the 
true size of the section and develop the lateral surface of the 
cylinder. 

Let Fig. 51 represent the top, front and left end views of the 
given cylinder. QQ is the top view of the given section plane. 

Find the points in which the elements of the cylinder 
piepce the section plane. 



These piercing points are first located in the top view, since 
this view of the section plane is a straight line. The front and 
side views of the piercing points are projected to the front and 
side views of the corresponding elements. 

Any number of elements may be taken so long as there is a 
sufficient number to determine the section figure. For conve- 
nience in construction twelve are usually chosen at regular in- 
tervals. 

The. element MN pierces the plane QQ at point B which is 




Fig. 52 

projected at B^ in the top view, at B'^ in the front view and at 
B^ in the end view. 

A smooth curve passing through the piercing points of the 
chosen elements forms the outline of the section. 

Since QQ is not parallel to either of the planes of projection 
the true size of the section is not shown. 

Rectangle WXYZ is drawn in QQ and its true size ( WXYZ)Q 
constructed as in Art. 31. 



Lay off (WBi)« = (WB)^ and (BiB; 



:BiB)^. All 



other points are located in the same manner. 

A smooth curve passing through the points thus located form 
the true outline of the section. 

In the development of the lateral surface of the cylinder, Fig. 



16 



52, the base rolls out into a straight line (GGi)'". The elements 
are located by stepping off the chord of the arc between them 
on (GGi)"*. The elements must be chosen near enough together 
so that the chord does not differ sensibly fi'om the arc. 






Fig. 53 

(GM)« = (GM)^. 

Lay off (GH)« = (GH)=. the true length of the element per- 
pendicular to (GGi)^. 

The completed rectangle (GHHiGi)^ is the development of 
the lateral surface of the cylinder. To find the outline of the sec- 



tion in the development lay off (GA)^ = (GA)^ and proceed in 
like manner for the points on the remaining elements. 

A smooth curve passing through the points thus located shows 
the outline of the section. 

33. To find the section of a regular square pyramid cut by a 
plane perpendicular to V and inclined to H and P. Show the 
true size of the section and develop the lateral surface of the 
pyramid. 

Let Fig. 53 represent the top, front and right side views of 
the pyramid. QQ is the front view of the given section plane. 

Find the points in which the edg"es of the pyramid 
pierce the section plane. 

These piercing points are first located in the front view, since 
this view of the section plane is a straight line. 

The top and side views of the piercing points are projected to 
the top and side views of the corresponding edges, thus: — 

The edge AV pierces the plane QQ at point M, which is pro- 
jected at M"^ in the front view, M^ in the top view and M^ in the 
side view. 

Straight lines joining the piercing point MNOL in order, form 
the outline of the section. 

Since QQ is not parallel to either plane of projection, the true 
size of the section is not shown. Rectangle WXNZ is drawn in 
QQ enclosing the section figure and its true size constructed as 
in preceding problems. 

On (XW)? lay off (XL)«=(XL)«. On (WZ)Q lay off (WO)Q 
= (L0)^. 

M'^ is located by laying off (XU)Q = (LM)^ on (XM)« and 
(UM)Q = (UM)H parallel to (XW)«. 

Lines joining points (LMNOL )^ in order, form the outline of 
the true size of the section. 

In the development of the lateral surface of the pyramid, Fig. 
55, the vertex remains stationary. The development is a series 
of isoceles triangles, the two equal sides of which are equal in 
length to the lateral edges and the third side is equal to the side 
of the base of the pyramid. 



17 



In order to construct the development, the true length of the 
lateral edgfes of the pyramid must be known. Since none of 
the lateral edges are parallel to either plane of projection it will 
be necessary to construct a line showing their true length. 

From Fig. 54 it may be seen that the altitude of the pyramid 
Wi and one-half of the diagonal ViA are the legs of a right tri- 
triangle of which the edge VA is the hypotenuse. Hence if the 
true length of Wi be laid off perpendicular to the true length of 



'\ 


\" 


II 


\\ 


II 


\ 


1 1 


\ \ 


I'l 


\\ 


1 1 


\ \ 


//tN 


\ \ 








H. \^ 




\ ^\.^ 


/ \ 


. >^ 


/ ^ \ 


\ jK 


/ \ 


* / \ 


1 


\ \ / \ 


1 


\ \ / \ 


1 


\ \ / \ 


1 


\ \ / > 


1 


\/ 




^A^ 




Fig. 54 

ViA and the triangle completed, the hypotenuse of the right 
triangle thus formed will be the true length of the edge VA. 

Point M is located on the true length line by laying off the 
distance VP along Wi and drawing MP parallel to AVi. In 
order to save the extra amount of labor and space this construc- 
tion may be superimposed on one of the orthographic views as 
in Fig. 53. 

Since the edges of the pyramid are equal in length, with V^ 
as a center. Fig, 55, strike an arc of radius (VB)'^= V^At, the 
true length of the edge as shown in Fig. 53. On this arc strike 
off chords (BC)«,(CD)«, (DA)« and (ABi)«, equal to the corre- 
sponding sides of the base. 



Lines joining points (VBCDABiV)^ in order, form the outline 
of the development. 

To determine the outline of the section in the development 
lay off (VN)«= V^Nt, the true length of VN. Locate points 
(OLMNi )^ in like manner. 

Lines joining the points (NOLMNi )'^ in order, form the outline 
of the section in the development. 

34. To find the section of a right circular cone, cut by a plane 




Fig. 55 

perpendicular to V and inclined to H and P. Show the true 
size of the section and develop the lateral surface of the cone. 

Let Fig. 56 represent the top, front and right side views of 
the cone. QQ is the front view of the given section plane. 

Find the points in which the elements of the cone 
pierce the section plane. 

These piercing points are first located in the front view, since 
this view of the section plane is a straight line. 

The top and side views of the piercing points are projected to 
the top and side views of the corresponding elements, thus: — 



18 



VN pierces the plane QQ at point C, which is projected at G^ 
in the front view, at C^ in the top view and at C^ in the side 
view. 

Any number of elements maj'' be taken so long as there is a 
sufficient number to determine the section figure. For conveni- 




ence in construction twelve are usuallj" chosen at regular inter- 
vals. 

A smooth curve passing through the piercing points of the 
chosen elements form the outline of the section. 

Rectangle WXYZ is drawn in QQ and its true size ( WXYZ)« 
constructed as in the preceding problems. 



Layoff (XU)'^= (XC)^and (UC)'2= (UC)«. All other 
points are located in the same manner. 

A smooth curve passing through the points thus plotted forms 
the true outline of the section, which is an ellipse. 

Since the elements of a right circular cone are all equal in 
length, the base rolls out into an arc of radius equal to the 
length of the elements. The true length of the elements of the 
cone is shown in (VP)"^, since VP is parallel to V. 

Strike an arc of radius (PV)k= (VP)^. Fig. 57. On this 




Fig. 57 

arc step off (PS)'^ equal to chord (PS)^. Continue this process 
until the periphery of the base is laid off along the arc. The 
angle which the chord subtends must be small enough that the 
chord does not differ sensibly from the arc. 

Since all the elements of the cone are equal in length, the 
right triangle formed by the altitude, radius of the base and any 
element is equal to triangle (VMP)'^. Hence to find the true 
length of VC it is only necessary to draw a horizontal line 
through C^ until it strikes (VP)^. (See Art. 33). (VCi)^ is 
the true length of VC. 

On (VN)«lay off (VC)« = (VCi)^. A smooth curve pass- 
ing through the points thus determined forms the outline of the 
section. 



19 



35. To find the section of a right circular cone cut by a plane 
perpendicular to H and inclined to V and P. Show the true 
size of the section and develop the lateral surface of the cone. 

Let Fig. 58 represent the top, front and left side views of the 
cone. QQ is the top view of the section plane. 




The section curve is hyperbola. 

86. To find the section of a right circular cone cut by a plane 
perpendicular to Vand parallel to an element of the cone. Show 
the true size of the section and develop the lateral surface of the 
cone. Fig. 59. 






Pig. 59 



Find the points in which the elements of the cone 
pierce the section plane. 

These points are first located in the top view, since this view 
of the section plane is a straight line. 

The general principles involved in the solution of the prob- 
lems are identical with those of the preceding problems. 



The method of procedure is the same as for problem in Art. 
34. 

The section curve is a parabola. 

37. To find the section of a sphere cut by a plane perpen- 
dicular to H and inclined to V and P. Show the true size of 
the section. 



20 



Let Fig. 60 represent the top, front and right side views of 
the sphere. QQ is the top view of the given section plane. 

Find the points in which a series of eircles on the sur- 
face of the sphere pierce the section plane. 

These circles are taken parallel to one plane of projection and 
therefore show as true circles on that plane, and as straight lines 
on the other planes of projection. 

The piercing points are first located in the top view, since the 
top view of the section plane is a straight line. The front and 
side views of the piercing points are projected to the front and 
side views of the corresponding circles. 

Circle SX pierces QQ at B, which is projected in the top view 
at B^, in the front view at B'^ and in the side view at B^. 

A smooth curve joining the piercing points of all the circles 
forms the outline of the section. 

The true size of the section is a circle of diameter (AE)^, the 
choi'd cut from the great circle by QQ. 

The surface of the sphere cannot be developed. 




E-^Q 





Fig. 60 



INTERSECTIONS 



38. When two solids intersect, the line common to the surfaces 
of both solds is called the line of intersection of the two solids. 

General Problem. To find the line of intersection of 
any two solids. 

General Method. Find the points in which the elements 
or edg-es pierce the g-iven surfaces. 

39. To find the line of intersection of two square prisms and 
develop their lateral surfaces showing the line of intersection. 

Let Fig. 61 represent the front, top and side views of the two 
square prisms- 

The points in which the edges of the horizontal prism pierce 



the faces of the vertical prism are first located in the top view, 
since in this view the lateral faces of the vertical prism are 
straight lines, thus: — 

IM pierces the face at AB at M, which is projected in the top 
view at M'^, in the front view at M"^, and in the side view at M^ 
on the corresponding views of the edge IM. 

M^ is best located by drawing the side view of the element in 
which IM pierces the face AB. 

The piercing points of the remaining edges of the horizontal 
prism are located in a similar manner. 

The points in which AE the edge of the vertical prism pierces 



21 



the faces of the horizontal prism are first located in the front 
view, since in this view the lateral faces of the horizontal prism 
are represented by straight lines, thus: 

AE pierces face OL at R which is projected on the front view 




A' 6' 



t 

N" 1 






Fig. 61 

at R^', in the top view at R", and in the side view at R'^, on the 
corresponding views of the edge A.E. The projections of S are 
located in a similar manner. 

Lines joining poiuts LMSNORL in order, form the line of in- 
tersection. 



The lateral sui'faees are developed according to the principle 
of Art. 31. 

40. To find the line of intersection of a right triangular 
prism and a cylinder, and develop their lateral surfaces showing 
the line of intersection. 

Let Fig. 62 represent the top, front and side views of the cyl- 
inder and prism. 






\ 








\^- 



M" 




Fig. 62 

Assuming elements in the faces of the triangular prism, the 
points in which they pierce the surface of the cylinder are first 
seen in the top view whei'e the lateral surface of the cylinder 
appears as a circle, thus: 

BM pierces the cylindrial surface at B, which is projected in 
the top view at B^, in the front view at B"^ and in the side view 
at B^. Any number of elements may be taken so long as there 
are enough to clearly determine the intersection line, which in 



22 



this case is a curve drawn thi-ough the common points on the 
two surfaces located as above. 

The lateral surfaces are developed according to the principles 
of Arts. 31 and 32. 



/ 


V^B- 


/I 


1 n 


/ / 


1 D-\— ' 



M-" 




Fig. 63 



41, To find the line of intersection of a right square pyramid 
and a right triangular prism, and develop the lateral surfaces 
showing the line of intersection. 

Let Fig. 63 represent the top, front and left side views of the 
pyramid and prism. 



Since the lateral faces of the pyramid are not seen as straight 
lines in either view, the points in which the elements and edges 
of the pyramid pierce the surface of the prism are found. These 
piercing points are first located in the front view, since this view 
of the lateral surface of the prism consists of straight lines. 

The edge OE of the pypamid pierces the surface of the prism 
at B which is projected at B'^ in the front view, at B" in the 
top view and at B^ in the side view on the corresponding projec- 
tion of OE. 

Elements may be taken at random in the faces of the pyramid 
and the piercing points found, but since the line of intersection 
will consist of a series of straight lines, only the points where 
the lines join need be found. Hence, the elements are chosen 
which intersect the edges of the prism. 

The front view M'^0'^ of the element MO is drawn through 
A"^. A^ is on the top view, and A^ on the side view of OM. 

The projections of points C and D are similarly located. 

Straight lines joining the points BAEDCB in order, from the 
line of intersection. 

The lateral surface of the pyramid is developed according to 
Art. 33, and that of the prism according to Art. 31. 

42. To find the intersection of a right circular cone and a 
right circular cylinder, and develop the lateral surfaces showing 
the line of intersection. 

Let Fig. 64 represent the top, front and right side views of 
the cone and cylinder. 

Since the lateral surface of the cone is not seen as a line in 
either view, the points in which the elements of the cone pierce 
the surface of the cylinder are found. These piercing points 
are first located in the top view, since that view of the lateral 
suface of the cylinder is a circle. 

The element O M, of the cone pierces the surface of the cylin- 
der at A, which is projected in the top view at A^, in the front 
view at A'^and in the side view at A*" on the corresponding pro- 
jections at OM. 

Elements mav be taken at random in the surface of the cone 



23 



and their piercing points found, but for convenience twelve are 
usually chosen at regular intervals and additional elements put 
in where it is desirable to locate other points. For instance B 




A smooth curve passing through the points located forms the 
line of intersection. 

The lateral surface of the cone is developed according to Art. 
34, and that of the cylinder according to Art. 32. 

43. To find the line of intersection of a sphere and a right 
circular cylinder. 






.o" 


A 


1 \^ 






\ \ \ 


\ \ \ 


\ \ \ 


I \ \ \ 


\ \\ ^ 


\ "^ \ 


\ \ ^ 


\ ^ '^^ \ 


\ \ \ 


\ \ \\ 


\ \ \\ 


\i ^ 





M 




Fig. 64 



the point in which the extreme element of the cylinder, in the 
front view, pierces the cone is an important point and should be 
located as above. 





Fig. 65 

Let Fig. 65 represent the top, front and left side views of the 
sphere and cylinder. 

Since only the surface of the cylinder is seen as a line, a series 
of circles are taken on the surface of the sphere and the points 
in which thej^ pierce the surface of the cylinder located. These 



24 



piercing points are found first in the top view, since this view 
of the cylinder is a circle. 

The circle CFOK pierces the surface of the cylinder at C which 
is projected at C^ in the top view, at C^ in the front view and 
at C^ in the side view on the corresponding views of the circles 
CFOK. The projection of points FOK in which circle CFOK 
also pierces the cylinder are located in a similar manner. 

Circles on the sphere may be chosen at random so long as 
planes are parallel to the elements of the cylinder and also to 
one of the planes of projection. 

Since two circles at equal distances on opposite sides of a 
great circle have the same diameter, the number of circles drawn 



in one view may be reduced, thereby simplifying the construc- 
tion. 

Care should be taken to locate critical points, for instance the 
points V and I, on the great circle, which are the points of tan- 
gency between the great circle and the line of intersection in 
the front view. 

A smooth curve passing through the points located as above 
forms the line of intersection. 

The lateral surface of the cylinder is developed according to 
Art. 32. The surface of the sphere is incapable of exact devel- 
opment. 



25 



CHAPTER 2 



FREEHAND LETTERING 



UPRIGHT SINGLE STROKE GOTHIC CAPITALS AND NUMERALS 



44. Elements of Letters and Numerals. The Gothic let- 
ters and figures are composed of either straight lines, ellipses, 
or combinations of the two. The straight lines are vertical, 
horizontal or oblique. For example the capitals H, T, L and 
others are composed of vertical and horizontal parts, the N, A, 
K and others are composed of inclined parts conbined with 
either horizontal or vertical parts, while the V, W and X are 
composed of inclined parts onlj-. The elliptical curves of the 
letters and numerals have vertical axes. These curves are tan- 
gent to the horizontal guide lines which limit the height of the 
letter. 

45. General Proportions. In general letters having dis- 
tinct upper and lower parts should have the upper part smaller 
than the lower. Intermediate horizontal lines should be placed 
slightly above the middle, except in the letter A where the hori- 
zontal part is one-third the height of the letter above the lower 
guide line. 

46. Quality of Line. All strokes should be made the same 
width. A pen should be selected that will produce strokes of 
uniform width in any direction. A slight imiform pressure 
should be brought to bear on the pen, not enough to spi-ead the 
nibs. The strokes should be made with a slow steady motion. 
Rapid strokes often produce a cleaner line at first, but with the 
result that the pen cannot be controlled to form the strokes cor- 
rectly. At first attention should be given to the form and direc- 
tion of the strokes and the proportions of the letters. Ability 
to produce clean, sharp strokes will be acquired by practice. The 



amount of ink carried in the pen is important. Too little ink 
makes it difficult to start the strokes. A stroke should not be 
started until the ink is seen on the paper or tracing cloth. The 
beginning and end of each stroke should be blunt. The pen 
should not be lifted from the drawing surface too quickly when 
the end of a stroke is reached. Too much ink in the pen will 
often cause blottino. Care should be taken to keep angles and 
intersections clean and sharp. It will be found that often an 
unsteady hand can make fair lines after a little practice. The 
pen should be tried frequently on a surface similar to the surface 
upon which the lettering is to be done. Short practice strokes 
about three-sixteenths of an inch in length will bring the ink to 
the end of the pen and will determine the kind of line the pen 
will make. 

47. Vertical Strokes. These strokes should be made eicac^/t/ 
vertical. A slight deviation from the vertical is very noticeable. 
All vertical strokes are made downward. Fig. 66. The vertical 



Fig. 66 

strokes are started on the upper guide line. In making these 
strokes the aim should be to reach a point directly under the 
starting point. As most of the letters have vertical strokes the 
manner of making them should be thoroughly fixed in the mind 
of every student. A tendency to slope the strokes forward, as 



26 



in inclined lettering, may be counteracted by attempting to finish 
the sti-okes slightly to the right of their starting points. 

48. Horizontal Strokes. Horizontal strokes are drawn from 
left to right. Horizontal strokes are drawn on or parallel to the 
guide lines- Fig. 67. 



and curves to the left a distance equal to one-half the width of 
the letter. The horizontal distance a, Fig. 69, is estimated. 



Fig. 67 

49. Inclined Strokes. The inclined strokes are made down- 
ward and to the right or left. In making inclined strokes the 
horizontal distances from the beginning of the stroke to the ver- 
tical line through the end of the stroke is estimated. Usually 
these horizontal distances have a known relation to the width of 
the letters. For example, in making the inclined stroke on the 
left side of the A the horizontal distance a. Fig. 68, is estimated. 
In this letter the distance a is equal to one-half the width of the 
letter. The second stroke ends the same distance to the right of 
the vertical center line of the letter. 




Fig. 68 

50. Curved Strokes. The curved strokes are parts of 
ellipses. The greater part of each curved stroke should be 
drawn downward or to the right. Avoid moving the pen upward 
or to the left wherever possible. The distances the curved strokes 
extend to the right or the left of their initial points is usually 
determined by the width of the letters. For example, the stroke 
forming the left side of the O is started on the upper guide line 



.j.^- 



Fig. 69 

51. Parallel Inclined Strokes. When two or more inclined 
strokes in the same letter are parallel their direction is deter- 
mined by the direction of the first stroke. The direction of the 
first of the parallel strokes should be carefully estimated. 

52. Vertical Center Lines. Some letters or parts of letters 
are symmetrical with reference to vertical center lines. In such 
cases the center lines need not be drawn, but their position 
should be in mind when the symmetrical strokes are made. 

53. Height of Letters. All strokes except the short straight 
stroke in the Q should be made within the guide lines. Upper 
horizontal strokes should have their upper edges on the upper 
guide line. Lower horizontal strokes should have their lower 
edges on the lower guide line. The upper and lower guide lines 
should always be drawn for the capital letters. 

54. Width of Letters and Numerals. For small single 
sti'oke Gothic letters the width of the H may be taken as four- 
fifths its height. The width of the H is taken as a standard. 
The E B N R S U and Z are the same width as the H. The C D 
G K Q T V and Y are a little wider. The width the of A X 
and M is equal to their height. Notice that when the height and 
width of a letter are equal the height appears greater. The 
letter W is the widest letter of the alphabet, its width being 
about one and three-quarter times the width of the H. The F 
P and L are slightly narrower than the H. The J is a narrow 
letter about four-fifths the width of the H. The I is the width 
of a single vertical stroke. The 4 is the only numeral that is as 
wide as the H. The 2 3 5 6 8 9 and ai-e narrower than the H. 



27 



Tlie 7 is the same width as the J. The 1 is a single vertical 
stroke. When the standard of width is small compared with 
the height, the letters and numerals are said to be condensed and 
when greater they are extended. Until the normal widths of 
the letters can be accurately estimated, a strip of paper with the 
width of the H marked on its lower edge will be found conven- 
ient. The strip may be placed over each letter during practice. 
55. Spacing". The spaces between letters should appear as 
nearly equal as the forms of the letters will permit. The spaces 
between the words and between lines of words should be suffi- 
cient to allow the words to stand out plainly. One and a half 
times the width of the capital H will usually be sufficient be- 
tween words. Some strokes are difficult to make on account of 
the fact that the spacing as well as their form and direction 
must be kept in mind at the same time. To illustrate, the left 
side of the O is formed by a stroke which begins on the upper 
guide line and curves to the left a distance which will leave the 
proper space between it and the right hand side of the previous 
letter. This stroke is formed and the letter spaced in one opera- 



tion. When strokes of this type are made their initial points 
should be carefully located. 

56. Position of Hand, Arm and Body. The pen holder 
should be held firmly as in writing. The forearm should rest 
upon the drawing board or the drawing table. Always stand 
when doing freehand lettering. The fingers of the left hand 
should be placed slightly to the left of the letters to be formed. 
A slight pressure of the left hand against the paper will place 
the body in a balanced position. This pressure will assist the 
right hand in securing the proper pressure of the pen on the 
paper. In making vertical strokes the forearm should be almost 
parallel to the strokes to be made, In making horizontal 
strokes the pen holder should be rolled slightly so as to secure 
lines of the same width as the vertical lines. In making inclined 
strokes the forearm should be shifted to a position almost par- 
allel to the direction of the strokes. The curved strokes are 
made with a combined finger and wrist motion. After some 
skill is acquired it will be found possible to make most of the 
strokes without changing the direction of the forearm. 



28 



FORM 


AND 




STROKES 




INCORRECT 


PROPORTION 


1 


2 


3 


4 


FORMS 




- — H — - 
























t 








/ 


/ 


























\ 


, 






/ 




















, 










\ 








/ 






















— 










\ 


i 






1- 


H 
















1 


/ 






/ 1 






/ 

/ 


1 --■ 


.... 


h- 




/-■ 


— 


/ 

/ 














/ 











57. 

A single vertical stroke. 



Narrower than the H . 



Slightly wider than the H. 



The horizontal bar is slightly above mid-height. 



Narrower than the H. Intermediate horizontal stroke slightly 
above mid-height and equal in length to one-half the width 
of the letter. 



29 



FORM AND 
PROPORTION 



-H 






STROKES 



I '■■,.■ 



E 



2 3 4 



^ 



K^ 



H 



S 



V 



INCORRECT 
FORMS 



H 



K7i 



S 



Z 



S 



M 



A 



The length of the lower horizontal stroke is equal to the width 
of the H. The upper horizontal stroke is slightly shorter. 
Intermediate horizontal sti-oke as in the H. 



The lower horizontal stroke is equal in length to the width of 
the H. The upper horizontal stroke is a little shorter. 
The right ends of the horizontal strokes are in the same 
vertical line. 



The same width as the H. 



The width and height are equal. The inclined strokes meet at 
a point one-fifth of the height of the letter above the lower 
guide line. 



The width and height are equal. The intermediate horizontal 
stroke is one-third the height of the letter above the lower 
guide line. 



.30 



FORM AND 
PROPORTION 








STROKES 



¥ 



E 



X 



^sr 



S 



W 



K 



X 



3 4 



M 



W 



Y 



ffiZ 



INCORRECT 
FORMS 



IZ 



w 



K 



X 



^T 



¥ 



SZ 



K 



Z 



Wider than the H. 



One and three-quarters times the width of the H. Strokes one 
and three are parallel and strokes two and four are parallel. 



Width at the top of the letter is equal to the width of the H. 
The width at the bottom is slightly greater. The second 
stroke intersects the vertical stroke at a point one-third the 
height of the letter above the lower guide line. The third 
stroke if produced intersects the upper end of the vertical 
stroke. 

Width and height are equal. The width on the upper guide line 
is slightly less than on the lower guide line. The inclined 
strokes intersect slightly above mid-height. 



Slightly wider than the H. 
mid-height. 



The inclined strokes intersect at 



31 



FORM AND 
PROPORTION 



S^U 



J 



STROKES 



T 



m 



i \) 



-LU. 



2 3 4 



13 



:sJ_ 



33 



I 



\.y 



m 



INCORRECT 
FORMS 



n 






n 



n 



u 



u 






Width same as the H. The vertical strokes are equal in length 
to two-thirds the height of the letter. The curved stroke is 
a portion of an ellipse. 



A narrow letter. The vertical stroke is equal in length to two- 
thirds the height of the letter. The curved stroke is a semi- 
circle. 



Slightly wider than the H. An ellipse. 



Same width as the O. The straight stroke extends a short dis- 
tance below the lower guide line. 



The oval is the same form as the 0. 



32 



FORM AND 
PROPORTION 



H 



7 




^ 



^ 



2 



1 



- ! ' !-— - JJ 



J_ 



STROKES 



-r^ 



\ --< 



U 



I 



■Tr 



or 



15 



K 



5 



INCORRECT 
FORMS 



S 



c 



K 



E 



K 



12 



E 



S 



The same as the C, with the addition of the short horizontal 
and vertical lines. The horizontal line is slightly above the 
center. 



Is slightly wider than theH. The length of the horizontal lines is 
equal to half the width of the letter. The cm'ved part is a 
portion of an ellipse. 



Slightly narrower than the H. The length of the horizontal 
portions of stroke two is a little more than two-thirds the 
width of the letter. The intermediate horizontal line is 
slightly above mid-height. The curved part is a semi-circle. 



Same as the P, with the addition of the inclined stroke. The 
inclined stroke begins at the end of the curved portion of 
stroke two. The width on the lower guide line is a little 
greater than the upper portion of the letter. 



The upper part of the latter is the same as the P. 
portion is somewhat wider. 



The lower 



33 



FORM AND 
PROPORTION 




STROKES 






S 



S 



K 



INCORRECT 
FORMS 



S 



e: 



Same width as the H. The form is based on two ellipses, the 
height of the upper being less than that of the lower one. 
The ellipses are tangent at a point slightly above mid-height 
The first stroke ends a little to the left of the right hand 
vertical tangent to the ellipses. The beginning of the 
third stroke is directly under the extreme left point of the 
upper ellipse. 

A little wider than the H. 



34 



FORM AND 
PROPORTION 







STROKES 



^. 



ET 



2 3 4 



^ 



z 



5 



Zi 



Z 



5 



INCORRECT 
FORMS 



ZE 



S 



5 



s 



A single vertical stroke. 



Same width as the H. The horizontal stroke is one- third the 
height of the numeral above the lower guide line. 



A nai-row numeral; the same width as the J. The second stroke 
ends one-third the width of the letter to the right of the be- 
ginning of the first stroke. 



Slightly narrower than the H. The upper part is elliptical in 
form. The curve crosses the vertical axis of the ellipse pro- 
duced a little below mid-height. The lower end of the 
curve is at right angles to the lower guide line. The upper 
width of the numeral is less than the lower, the contraction 
being on the left side. The horizontal stroke ends directly 
under the extreme right point of the curve. 

Narrower than the H. The length of the first stroke is one- 
half the height of the numeral. The second stroke is almost 
a complete ellipse. The third stroke ends at a point slightly 
to the left of the extreme right point of the ellipse. 



35 



FORM AND 
PROPORTION 



•H- 







STROKES 



<ri! 



H? 



'^■ 



m 



(fi-. 



3 



J 



S 



m 



s 



INCORRECT 
FORMS 



Z 



5 



E 



2 



S 



2 



n 



s 



s 



a 



Narrower than the H. The form is based on two ellipses; 
the upper one smaller than the lower. The end of stroke 
two is slightly above the center. 



Narrower than the H. An ellipse. Notice that the zero is de- 
cidedly narrower than the letter 0. 



m, 



Narrower than the H. The form is based on an ellipse like the 
zero. The third "stroke extends above mid-height. 



Narrower than the H. The form is based on an ellipse, 
first stroke extends below mid-height. 



The 



Narrower than the H. Two ellipses; the upper one smaller than 
the lower. The ellipses are tangent to each other at a point 
slightly above mid-height. 



36 



FllilSHED 


STROKES 1 


LETTER 


1 


2 


3 


4- 


/ 


ZIL 


III 


111 




/ 


J.L 

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1. 








— *• 






T 


7^ 
















H 


h 


1 h 


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— > 


W 





F 


h 


r 










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E 

Z 


./i... 




£1 








N 


li 


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A/ 




M 


Ill 


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M: 













FmiSHED 


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LETTER 


1 


2 


3 


4- 


A 


y- 


■-^-s 


;;^; 






#,. 








V 


v^ 


l/"/ 






W 




jy- 


W" 


vi 












K 


h 


/^ 


::/^::. 














X 
Y 


.A. 






- 




'■ 


■■' 






U 


M.:. 


.LM 


.^^. 










^-»^ 




J 


:M::: 


.,./. 






O 


> 

■t 



















FllilSHED 
LETTER 



Q 

c 

G 
D 
P 
R 
B 
5 
& 



STROKES 1 


1 


2 


3 


■tl 


Ipl 


i^i 


m 


:;^ 








h 


/7' 






> . 




/> 


.^>:: 








7?;" 


/' 


:^:i 




.... ">.J 


igf 


/> 


:.yt^:: 


■^ 


:;:# 


zs:. 








A 


.<^. 











37 



SCALE 


or 


MIGHTS 1 


Tr\D 1 1 WF 






-HEADLINE 
-BASE LINE 


1 Ur LIINL — ./:: 

1 n\A/FR 1 1 M F— V.V.V. 


^ 


ii?- 









FINISHED 
LETTER 



/ 



/ 

z 

V 

w 

X 

y 



STROKES 


9 


SLOPE 


1 


2 


lUNIT / 

i f 

l/\ UNIT I lol 


"::.:'/:'." 




// 






i 


, 


/' 


/ 


''='W 








^/^" 




STROKES 1 


-» 




3 


4- 






// 


z 




1 


7 


-*■! 




|/v 


I// 






:::.fLZ 


";;.y/::.: 


::Mr. 


..^ti/i": 


\\ 


:::::^:: 














\Lk 


";;w;; 






/ 


.i.-j^:;::::: 







FIMISHED 
LETTER 



k 

# 

y 

/ 

r 
h 
n 
m 
u 





STROKES 


1 


2. 


3 


1r' 


■:::h::^ 


^^ 


ah 


i 




■¥--- 


■ 


:r:r^:^ 




:::::/:,::. 


:^^:: 










h 


-^jr- 






1 


77?"^ 


'j'c: 


-:f1^ 








:::i:r.::: 


""Oir: 


....4/._. 


-^(ir- 


0/" 

-4r 


^-» 









FiniSHED 
LETTER 



c 
e 
a 
d 

9 
b 

P 
s 



STROKES [ 


1 


2. 


3 


. id 








4' 




::::^^::. 




■■-0-r 


zw::. 






:3r 


01 










4 






: 







38 



UPRIGHT ARABIC 



FINISHED 
hUMERAL 



4 
7 
2 



3 




8 



STROKES 1 


1 


2 


3 








. i 






;;z< 


:"::4S: 


"4' 


...__.... 






7/ 




1 
<-• 


,:^- 


Ti 


1 










-i 


:::\:}:^: 


.::fe;r. 


...b 


-:.li-:—- 


■-.vi):.l-: 


:4)" 


:iz 


"iii: 




i > 

■ v.v: .">'. w ' ■ 


1$: 


:M 


;^&:;:: 


;;;ii 


::k: 


::i>;;;: 


:;:$:; 


M 



WIDTH 



I4i 

pi 
i2i 



I3i 

lol 



m 



INCLINED ARABIC 



FINISHED 
NUMERAL 



/ 
4 

7 
2 
5 
3 

6 
9 
8 



STROKES 1 


1 


2 


3 


/ 






1' 






i 






zzr 


";;z?' 


"W 


-' 


■y/ 




4' 






'^L 


B 








;;j:r 


10:. 


151 


"".'.\'/7".'" 


-:::m: 


:^f 










"::$L 






mi 


::m. 


::;i^: 


IM. 




■iSi 


::;;#: 


:i$i 



ROMAN 



FINISHED 
NUMERAL 



I 

I 
I 

V 

VI 

VI 

VI 

K 

X 



5TR0KE5 



::tii: 

I -» 3l 

ill: 
iii: 

Ml 

[::iii: 



wm, 



v¥ t 



:/A^- 



MISC. 


:.vr^-;;: 


:mi 


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IM: 


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.:4;-v 

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":ix: 
pi 



39 



CHAPTER 3 



WORKING DRAWINGS, INSTRUMENTS AND CONVENTIONS 



58. InstPUments. The thing of prime importance to the 
student in beginning drawing is a good set of instruments. He 
had better have a fewer number and those of standard quality, 
than a variety of poorly constructed, cheap instruments. Begin- 
ners often think that a cheap set will do to learn with and a good 
set can be secured afterward. But it must be emphasized that 
while the student is learning is the time when he forms his draft- 
ing habits and sets his standard of excellence. He is inexperi- 
enced in handling the drafting instruments and hence, to obtain 
the best results, the best instruments are none too good. With 
a good set of instruments he is able to reach a degree of excel- 
lence consistent with his ability; he has a fair chance to make 
good, while with a poor set he is handicapped from the start, 
and can never obtain the results he might have obtained with a 
better set. It is difficult to define a "good" set of instruments 
so that the beginner will recognize them, for the better grades 
are extensively imitated, and he should be guided in his selec- 
tion either by some more experienced draftsman, or the trade 
mark and the price set by some reliable dealer. 

A good set differs from a poor one mainly in, that they are 
made of better material, are tempered correctly so that when 
once sharpened will remain so for a reasonable length of time, 
and the workmanship is such that they retain their alignment 
and adjustment when handled with reasonable care. These 
things can only be known definitely after the set has been given 
a fair trial. 

Next to a good set of instruments is this consideration: theij 
must he taken care of, — for as with any other delicate mechan- 
ism, the best results can only be reached when care is taken in 
their adjustment and the working parts kept in prime condition. 



It is often difficult to impress upon the student the importance 
of having a ruling pen or needle point sharp, or a compass joint 
nicely adjusted, but after some experience he will surely agree 
that perfection can never be attained with imperfect or poorly 
adjusted instruments. 

59. Speed, Accuracy, and Neatness. The requisites for 
a good draftsman are speed, accuracy and neatness. The good 
draftsman combines accuracy and speed by a judicious handling 
of the instruments and a studied method of procedure. He does 
things in the most economical order. He looks ahead as far as 
possible and groups like operations so as to avoid unnecessary 
handling and adjustment of instruments. As far as possible 
all circles of the same radius are drawn while the compass is in 
the hand; all possible measurements are laid off from the scale 
at one time, etc. 

All straight edges, angles, scales, etc., should be carefully 
tested, joints of instruments kept in good order and their points 
sharp; then by careful handling, fine lines and points in their 
proper positions may be secured in the drawing. The time used 
in sharpening pencils and keeping the instruments in good order 
is well spent. 

Errors multiply with the number of operations involved, so 
other things being equal, the most direct construction is the 
most accurate. The location of points by very oblique intersec- 
tions should be avoided- 

The student should always sacrifice time to accuracy; speed 
will obtain through practice. 

To secure neatness, the instruments should be kept clean, and 
in good working condition, and blotting and erasing should be 
avoided. Orderly habits aid greatly in securing neatness of work. 



40 



PLATE 1 



EXERCISES WITH TRIANGLES, T-SQUARE, SCALE AND PENCIL 



60. Drawing" Boards. The drawing board should be made of 
well seasoned, straight grained, soft wood; free from knots and 
cracks. The best boards are designed to prevent warping, vari- 
ous means being used to accomplish this end. Some are built 
up of small sti'ips glued together; others have a series of saw 
cuts in the back running lengthwise of the grain to reduce the 
transverse strength and are made rigid bj'- cleats of hard wood 
screwed through slots equal in width to the diameter of the 
screw. This arrangement allows the board to expand and con- 
tract, the screws sliding back and forth in the slots. 

(a) Tests. To test the surface of the board place a standard 
straight edge upon it in vai-ious positions and with the board 
held up to the light notice whether the straight edge is in con- 
tact with the surface at all points. Test the working edge of 
the board similarly. 

(6) Care. The surface and edges of the drawing board 
should be kept free from cuts, scratches, and bruises. Paper 
should be cut on the hack of the hoard. The board should not be 
subjected to extremes of temperature and moisture. 

61. The T- Square is used for drawing parallel horizontal 
lines, and for directing the motion of the triangles. It consists 
of a rule called the blade attached to one end of which is a 
cross-piece called the head, which directs the motion of the blade 
b}' being pressed against the edge of the board. Lines are 
alwaj's ruled along its upper edge. The head is sometimes made 
movable so as to draw parallel lines in any direction. The blades 
are made of various kinds of wood, and of steel, or rubber. 
The most common forms are made of wood with edges of 
ebony, or celluloid. The steel blade is the most accurate, but 
tends to soil the drawing and smear dry ink lines. 



The requirements are that the under surface of the blade shall 
be plane, and the working edge of the head and blade straight. 
It is not necessary that the edge of the blade be at right angles 
to the head. 

(a) Tests. The best method for testing the edges of a 
T-square is a comparison with a standard straight edge. The 
edges of the blade may be otherwise tested as follows: Draw a 
line along the edge of the blade through two points on the paper, 
and mark the position of the end of the blade. Now swing the 
square around to reverse the ends of the blade with respect to 
the ruled line, keeping the same side up and bring the same 
edge to the ruled line, with the end on the mark and rule a 
second line through the two points. If the two lines coincide 
the blade is straight. In using the square the head should be 
held firmly against the edge of the board with the left hand, the 
ruling being done with the right. 

[b) Care. Great care should be taken to preserve the square 
from injury. The upper edge should always be used for ruling, 
and should be kept free from cuts and bruises. It should never 
be used as a guide for the knife in cutting paper. If a straight 
edge is necessary in trimming drawings use the lower edge. 

62. Triangles are used for drawing perpendiculars and lines 
at various angles, and for ruling parallel lines. They are made 
of wood, rubber or amber. The rubber and amber are the more 
accurate and the amber has the double advantage over the rub- 
ber that it does not attract dirt and soil the drawing, while it 
permits the lines to be seen through it. The forms most com- 
monly used are the 45° and 60° triangles. With these any 
multiple of 15° can be constructed. Other forms are used for 
special purposes. 



41 



(rt) Tests. The edges of a triangle should be straight and its 
angles true. The edges are best tested with a straight edge, — 
otherwise by reversion as explained for the T-square. The right 
angle may be tested as follows: Place the triangle in position 
D as shown in Fig. 70, and draw the line AB. If when the tri- 
angle is tui'ned over into position C, the edge coincides with the 
line AB the angle is 90°. 

When the right angles have been found true, the 45° angles 
are true if equal, and the 30° and 60° are true if one is double 




Fig 70 

the other. These points may be tested by constructing the 
angles on paper thus: For the 45° angle draw a 45° line with 
one of the angles and bringing the other into the same position 
see if the edge coincides with the line. For the 30°, 60° tri- 
angle place the short leg against the T-square and draw two 60° 
lines through a point by reversing the triangle so that the lines 
make angles on opposite sides of the vertical. Fig. 70. Now 
draw a horizontal line cutting the two lines- If the triangle formed 
is equilateral, which may be ascertained with the dividers, the 
60° angle, and also the 30°, is true. 




Fig. 71 




Fig. 72 

(b) Triangle and T-square Combinations. To draw lines 
maMng 15°, 30°, 45°, 60°, and 75°, ivith the horizontal. Figs. 
71 and 72. 



42 



I 



In drawing a line through a given point in a line the T-square 
should be moved away from the line so that the edge of the tri- 
angle passes through the point. This principle holds in any 
combination. The straight edge which guides the motion of the 
ruling edge should not pass through the point through which 
the line is to be drawn. 




Fig. 7;5 

(c) Triangle Combinations. Lines parallel or perpendic- 
ular lo an oblique line, or making with it angles of 15 , 30 , 45 
60°, and 75°. 

For example, to draw a line parallel to AB through C. Fig. 



73 A. Place triangle D so that one edge coincides with AB and 
fit triangle E against it. With E held firmly in place by the left 
hand slide D along until the edge passes through C. 

lu Fig. 73 the black triangle represents the fixed triangle and 
the dotted one is the movable one set upon the line. The full 
line shows the position in which the movable triangle guides the 
pencil, or the position of the triangle substituted for it. 

63. Scales are used for making measurements and laying off 
distances. They are made of paper, ivory, boxwood, rubber, 
and steel, and are divided into all convenient units. The usual 
forms are the flat, with beveled edges, and the triangular. 

The scale should be perfectly straight, the edges should be 
thin, sharp and free from nicks, and the graduations very fine 
clear-cut lines. The scale is usually a little over 12" long, and 
is graduated for a distance of 12". 



{ 



3 6 9 



Fig. 74 

(rt) The architect's scale is divided on one face into inches, 
halves, quarters, eighths and sixteenths of an inch. The other 
five faces of the triangular scale have two scales each, one being 
one-half the other. To illustrate the reading of these scales, 
consider the one designated by a figure 1 at the end, which indi- 
cates that the scale reads 1 foot for each inch of the scale. The 
inch to the right of the at the right end is divided into 48 
equal parts so that each of the smaller divisions represents Y\ 
and the spaces marked 3, 6, 9 represent 3" each. To the left 
of the the readings 1, 2, etc., ai-e inches, and of course rep- 
resent feet. Now to measure off for example a distance of 2 ft. 
45" its. to the right of a point, Fig. 74, place the 2 opposite the 
point X and read to the right past the 0, 4^ ins. to the point Y. 



43 



In case you wish to read to the left place the 4^ in. mark to the 
point and read to the left through to the 2. 

The scale should never he used as a straight edge in ruling 
lines. 

64. Pencils. The lead of the drawing pencils should be of 
fine, even grain and of a hardness suited to the paper upon which 
the drawing is to be made. It should give a fine, firm, clean-cut 
line without pressure enough applied to crease the paper, so that 
in case it is necessary to erase no marks are left to disfigure the 
drawing. These properties may best be determined by trial. 
For the Duplex paper a 4H to 6H will be found suitable for the 
mechanical line work, and for the freehand work — letters and 
figures, a 2H to 4H is satisfactory. 

65. Sharpening- the Pencil and Compass Leads. The pencil 
point is one of the things most neglected by beginners and yet 
it is one of the most important of all the drawing instruments, 
requiring frequent and patient attention to secure good results. 
A dull or improperly sharpened pencil is not only inaccurate, 
but produces a mussy drawing, a thing which is almost certain 
to give an unfavorable impression of the student's ability as a 
draftsman. 

(a) The Ruling Point. For ruling lines the wood should be 
cut away until about f" to i" of lead is exposed and this should 
then be ground to a chisel shaped point by rubbing opposite 
sides on a fine file or sand paper pad, holding the pencil at an 
angle of a few degrees to the plane of the pointer. Having pro- 
duced a thin edge, round the corners slightly by rotating the 
pencil about its axis slowly while the former grinding motion is 
continued. Fig. 75. Compass leads should be sharpened in the 
same manner. The chisel point is particularly effective where a 
large number of long lines must be drawn. 

(b) The Measuring Point. For laying off distances the point 
should be conical and very sharp. It is a good plan to sharpen 
one end of the pencil for ruling and the other for measuring. 
For freehand work the point should be conical but somewhat 
more blunt than the measuring point. 



(c) Manipulation. The pencil should always be pressed very 
lightly upon the paper. In ruling along a straight edge care 
must be taken to hold the pencil constantly at the same inclina- 
tion to the paper; i. e., move it parallel to itself. This is 
necessary in order that the line drawn be straight and parallel 
to the ruling edge. The rule should be flat upon the paper. Points 
should not be obliterated with pencil lines. If several lines are 
to be drawn through a point it is better to stop them a short 
distance from the point, so as to leave it clearly defined. A 
small circle should be drawn around points to indicate their 
position instead of making the points heavy. 




Fig. 75 

66. Dividers are very similar to compasses in general appear- 
ance, the difference being that they usually have no lower joints, 
and that they have two very sharp points of steel. When closed 
they have the appearance of a single conical point. They are 
used either for laying off distances from the scale, or for trans- 
ferring lengths from one part of a drawing to another. They 
may also be used to divide a line either straight or curved into 
any number of equal parts. 

(a) Manipulation. A line is divided into a small number of 
equal parts by trial. First the required fractional length is 
estimated and then stepped off on the line. If it is not correct 
the first time an adjustment is made according to the size of the 
error. In stepping off distances on a line the dividers should be 
held by the handle between the thumb and forefinger, and swung 
alternately on one side of the line and the other. The plane of 
the legs should be perpendicular to the paper. 

Do not make large holes in the paper. 

67. Paper. The requisites of a drawing paper depend upon 
the character of the drawing to be made, and we need only con- 



44 



sider the qualities essential to a paper suitable for ordinary shop 
drawings. 

The paper should be strong, and must stand erasure without 
spoiling the surface. As the drawings are to be traced the inking 
qualities need not be considered. Whatman's hot pressed is 
very satisfactory for precise line drawings. It has a smooth 
surface and stands erasure very well, but on account of being 
expensive is not much used in commercial drafting offices. 
Detail paper comes in rolls and is much cheaper and of inferior 
quality, but quite extensively used in office practice where work- 
ing drawings are to be made and traced. It is of buff color, 
has a smooth surface and does not stand erasing very well. An 
excellent paper for fine pencil drawings is the Duplex. There 
are many styles and makes of paper on the market each 
having its particular advantages and disadvantages, for a descrip- 
tion of which see dealers' catalogue. 

68. Starting" the Work. The first thing in order is to fasten 
the paper on the board. This is best accomplished by inserting 
a tack in the upper left hand corner, squaring it on the board 
with the T-square against the lower edge and then stretching it 
diagonally across to the other corner and inserting a second 
tack; now stretch it diagonally the other way and fasten as 
before. This method of procedure will insure the paper being 
stretched smooth and flat. 



It will be found awkward to use the T-square near the lower 
edge of the board, and hence when the paper is smaller than the 
board it should be placed well above the lower edge. 

69. Size of Plates. The finished plates are 11'' x 15" ; the 
rectangular area enclosed by the border line is 10" x 14", thus 
providing a \" space l)etween the border line and the edges of 
the plate. The border line when drawn in pencil is a good, 
sharp, clean-cut line. In fastening the paper to the drawing- 
board — if the sheet is previously cut to about 11" x 15" — the 
thumb tacks should pierce the paper \" from each of the two 
edges. Upon removal from the board, the thumb tack holes 
should be closed by pressing back into place the paper disturbed 
by the tacks. If the sheet is larger than 11" x 15", the tack 
holes should not show in the finished plate. 

70. To lay out the Border Lines. Lay out the 10" x 14" 
border line as follows: Working from the upper left hand cor- 



ner of the sheet measure down 



from the same corner 



measure \" to the right. Draw a horizontal line through the 
first point and a vertical line through the second, thus locating 
two sides of the 10" x 14" rectangle. From the ujiper left hand 
corner of the border line lay off 14" to the right and 10" down, 
and through the points thus located draw the remaining sides 
of the rectangle. 



45 



PLATE 

Make a complete pencil drawing of the figures as shown on 
page 47. 

71. Fig-ure 1. Page 47. Draw a horizontal center line for 
the sheet and on this center line measure 4" to the right from 
the left border line. This will locate the center of Fig. 1. 
Through this point, using the triangle against the T-square, and 
the wedge-shaped lead of the pencil, draw EF perpendicular to 
the horizontal line. With the 45° triangle against the T-square 
draw AB. All lines should be drawn very light, no attempt be- 
ing made to draw them of definite length. They may be gone 
over afterward, made more distinct and of the proper lengths. 
With the scale and the sharp conical point of the pencil lay off 
1" on each side of the center on AB. Through these points 
draw CE and FD perpendicular to AB. These lines will also be 
at 45° to the horizontal. Through the points where CE and FD 
strike the horizontal and vertical lines, draw ED and CF at 45° 
to the horizontal and parallel to AB. 

On all four sides of the square thus formed lay off \" spaces 
with the scale and sharp conical point of the pencil. In the tri- 
angles formed by the diagonals of the square and its sides draw 
alternate full and dotted lines as shown. Refer to Fig. 83 for 
methods of joining lines. All lines should be full and very light 
at first. Those that are to be dotted will be made so when the 
lines are gone over. Omit all letters and dimensions from the 
finished plate. 

72. Fig-UPe 2. Locate the center of Fig. 2 as shown. Draw 
LM at 30° and ON at 60° to the horizontal. Draw PQ at 75° to 
the horizontal and on it mark points 2" on each side on the cen- 



ter of the figure. Through these points draw LN and OM, per- 
pendicular PQ, or what is the same thing at 15° to the horizon- 
tal. Through the points where these lines strike the 30° and 60° 
lines draw lines parallel to PQ (at 75° to the horizontal.) Lay 
off y spaces on all four sides of the square thus formed. In 
the triangles formed by the sides of the square audits diagonals, 
draw alternate full and dotted lines, as shown. 

Draw the filing circle in the lower left hand corner of the 
sheet and letter therein the appropriate plate number, and filing 
number, using the dimensions as given in Fig. 75 A. Omit the 
sheet number. Add the initials below the filing circle, keeping 
the lines of figures and letters symmetrical with reference to an 
imaginary vertical line through the center. 

73. Title. Letter the word "Exercises" in the lower right 
hand corner of the sheet, ^" above the border, and \" from the 
right border line- The letters should be \" in height. 




Fig. 75 A 



Refer constantly to pages 29-36 when maling the letters and 
numerals in the above. 



46 



4" 



6t 




FIG 2 



/go 2^ 



UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRA\A/lNG 
COURSE I 



47 



PLATE 2 



EXERCISES WITH TRIANGLES, T-SQUARE AND RULING PEN 



74. Ruling- Pen. This is most used of all the instruments 
and should therefore claim considerable attention in its selection, 
manipulation and care. It is used for ruling lines in ink. 

(a) Construction. It consists of two blades of steel connected 
by a screw for regulating the distance between the points, and 
these surmounted by a handle of wood, ivory, bone, or alumi- 
num. One of the blades is usually provided with a joint or 
other device by means of which the blades may be spread apart 
for cleaning. The qualities that a ruling pen should possess are 
as follows: The steel should be of such quality as to retain a 
smooth sharp edge; the blades should be of the same length, and 
the inner one sufficiently stiff to resist a light pressure against 
the ruler; the points should be of the same width equally 
rounded and directly opposite each other. 

(6) Manipulation. In using the pen it should be held in a 
plane perpendicular to the sui-faee of the paper, the handle in- 
clined a little to the right and the blades in a plane parallel to 
the ruling edge. It is held between the thumb and first and 
second fingers, the knuckles bent so that it may be held at right 
angles to the length of the hand, and with the points of the pen 
pressing lightly upon the paper. With the pen in this position 
draw it rather slowlj^ from left to right. The motion should be 
one of the shoulder and elbow without bending the wrist. Keep 
the forearm always perpendicular to the line being drawn, at 
whatever angle to the horizontal. Endeavor to get into the easiest 
position for inking a line, even though it becomes necessary to 
walk around the drawing. The best results are secured by 
standing while inking. Care should be taken that the points of 
the nibs do not approach the ruling edge too closely or the ink 
will be drawn under by capillary attraction. When the line is 



inked move the ruling edge away from it to avoid blotting. Do 
not press the side of the pen point too heavily against the ruling 
edge, as the nibs will be pushed together and the width of line 
will vary. A certain touch, familiar to good draftsmen, brings 
the pen lightly but firmly in contact with both the .cloth and the 
ruling edge. Steady the hand by sliding it on the end of the 
little finger. The pen should be moved from left to right, and 
should be drawn, not pushed. 

(c) Blotting. With care blotting may always be avoided. It 
may be caused by (1) ink flowing under the rule by capillary 
attraction, (2) moist ink on the outer surface of the blade in 
contact with the ruler drawing ink by capillary attraction from 
between the nibs and finally to the paper, (3) touching the 
edge of the rule with the point of the pen in lifting it from the 
paper, (4) by drawing a line over a moist portion of the paper 
or over one that has been roughened by erasing, (5) filling the 
pen too full so that the ink is not sustained by capillary attrac- 
tion. 

(d) Filling the Pen. The pen is filled by drawing the quill 
attached to the stopper of the ink bottle between the nibs. 
When filled the ink should not stand more than i" to f" from 
the end of the nibs to avoid blotting. When the ink does not 
flow freely from the pen it should be removed, the pen thor- 
oughly cleaned and supplied with fresh ink. 

(e) Care. Clean the pen while in use by inserting a piece of 
cloth between the blades and drawing it out through the nibs 
without moving the thumbscrew. Ink dries quickly so that the 
pen should not be laid aside for any length of time without 
cleaning. After using the pen it should be carefully cleaned by 
separating the nibs and wiping with a piece of chamois skin or 



48 



one of the pen wipers which come with prepared inks. If the 
ink is allowed to corrode it may ruin the surface of the nibs, 
thereby spoiling the pen. 

(/) Setting and Orinding the Pen. The blades should be of 
precisely the same length, the points of the same width, rounded 
in two directions, and as sharp as they can be made without 
producing the sensation of cutting. They should not scratch 
the paper when drawing a line. This occurs if they are sharp- 
ened to a point instead of a rounded edge, or if the point is 
rough or notched. Any irregularities in the length of the points 
may be detected by holding the pen up to the light so as to see 
both points, and then closing them slowly. 

In case of irregularities or the pen becoming dull from use it 
may be treated as follows: Close the nibs until they just touch 
each other and then, using a close-grained oil stone, hold the 
pen as though to draw a line and draw it back and forth, revolv- 
ing it slowly in the plane of motion which is perpendicular to 
the plane of the stone. This will dull the nibs, but it will grind 
them into the desired rounded point. Grind until the nibs are 
of equal length. If the pen now be held up to the light with 
the nibs separated and the points directed to the eye so as to 
catch the angle of reflection of the light, a bright speck will be 
seen on the points. This must be reduced by rubbing the out- 
side of the nibs on the oil stone, giving at the same time a slight 
rotary motion to the handle, which is held at an angle of 16° or 
20° with the face of the stone; the point of the pen being exam- 
ined from time to time, and the process continued until the 
point is as fine as can be used without cutting the paper. 

All grinding should be done on the outside of the nibs. To 
remove the burr from the inside use a piece of leather or soft 
pine. 

75. Erasure. Many students find trouble in erasing from 
the tracing cloth without marring the drawing. If proper care 
is taken ink may be erased so that the surface of the cloth is 
hardly affected. A shield of brass or celluloid should be used 
and the opening in it which best fits the line or spot to be erased 



selected. By holding it firmly with the fingers of the left hand 
and employing an ordinary pencil eraser in the right, the ink 
will readily yield. Finish by polishing with a smooth surface 
such as the thumb nail, a piece of ivory or soapstone. 

76. Tracing" Cloth is the medium most generally used for 
reproducing the original drawing in the form of prints. It is a 
firm transparent cloth covered with a sizing. The side on which 
the sizing is placed is verj'^ smooth and glassy, while the other 
side is less so. 

The time worn question of which side of the cloth is to be 
used is best decided by considering the nature of the work to be 
done. The glazed side was primarily intended for use and 
hence was rolled in, but the cloth will curl when inked on this 
side. From the fact that there is more sizing on the glazed 
side, the ink, especially red ink, does not eat so deeply into the 
cloth and hence is more easily erased from this side. If work is 
to be done in pencil it must be done on the dull side in order 
that the pencil lines show. The dull side takes ink more readily, 
without so much danger of blotting, and the cloth does not curl. 
In general it is safe to say that where much erasing is to be done 
the bright side is preferable, but where penciling is to be done 
on the cloth the dull side must be used. Beyond these consider- 
ations the choice rests entirely with the draftsman. 

If the surface of the cloth appears greasy so that it does not 
take the ink readily, it should be either washed with gasoline or 
benzine, or be rubbed with finely powdered chalk, taking care 
to remove all of the chalk before trying to ink again, as it will 
clog the pen. It may be washed with gasoline or benzine to remove 
pencil marks or smudge after the drawing is finished, without 
affecting the ink. 

Tracing cloth is affected by the moisture of the air which 
causes it to stretch, and water will ruin it. 

77. Blue Print Paper is made of several different grades of 
white paper covered with a coating sensitive to light. In print- 
ing, the inked side of the tracing should be placed next the glass 
in the frame or machine, and then the sensitive side of the paper 



49 



next the tracing. They are held tightly in this position by a 
board or cloth, and exposed to a bright light for a time, depend- 
ing on the "speed" of the paper. That part of the coating 
protected from the light by the lines on the tracing is washed 
away when the print is placed in water while the exposed por- 



tions turn blue; hence the i-esult is white lines on a blue ground. 
These prints may be mounted on a smooth fiat surface and 
given a coat of shellac, thus forming very durable shop draw- 
ings. 



PLATE 2 



Make a complete tracing of Plate 1. 

78. To Stretch the Tracing- Cloth. Use the dull side of the 
tracing cloth. It is cut slightl.y larger than the drawing paper 
and the greater pai^t of the extra area is to be left at the top and 
right hand sides. This extra area is used to try the pens on, 
before inking in the work. Remove the lower left hand tack 
fi'om the drawing. Place the tracing cloth over the drawing so 
that it extends about ^ beyond the lower and left hand edges 
of the paper. Insert the tack into the hole that it previously oc- 
cupied. Remove the tack from the upper right hand corner of 
the sheet. Stretch the tracing cloth diagonally, and insert the 
tack as before. Proceed in a similar manner with the other two 
corners. The tracing cloth should lay flat on the drawing pa- 
per. If tracing cloth is allowed to remain on the board some 
time its surface becomes uneven on account of changes in the 
atmosphere. If the cloth becomes uneven it should be restretched 
as described above. The tracing cloth should not be fastened 
over the drawing until the tracing is to be started. 

79. Lines. Both the full and the dotted lines should be ob- 
ject line weight or g-V in width. It is good practice to ink the 



squares, rectangles and triangles until not only the lines are 
good, but the corners and intersections as well. Corners should 
be very definite. Be careful to stop each line at exactly the right 
point, for ragged corners and poor intersections indicate careless 
work. 

Border Line. The border line should be a heavy black 
line y/' ill width on the tracing. 

80. Pencil Guide Lines. The student should rule guide lines 
for all lettering, using a 3H pencil. Guide lines ruled on the 
drawing paper will not answer when lettering on the tracing 
cloth. Ruling the guide lines on the surface to be lettei-ed gives 
better results. 

The tracing cloth should be cai-efully cleaned with a soft rub- 
ber in order to remove all pencil and other marks before blue 
printing. A hard eraser should not be used for cleaning pur- 
poses as it will remove the ink from the lines of the drawing. 

81. To Cut the Tracing" Cloth to the required size, after the 
drawing is completed, use a very sharp knife. The working 
edge of the T-square should not be used to guide the knife. 



50 



PLATE 3 



EXERCISES WITH COMPASS AND BOW PENCIL 



82. Compasses are used .for drawing circles or arcs of circles. 
For very large circles the lengthening bar may be added, and 
when this does not suffice, a beam compass may be used. The 
bow compass is best for circles under f'" radius. 

(«) Construction. They are best made of rolled German sil- 
ver, and should combine lightness with rigidity. The vital part 
of the compass is the head which in the modern instruments 
consists of two discs forming the heads of the legs held in appo- 
sition in a fork by means of two pivot sci'ews, which also serve 
to adjust the bearing. The top of the fork terminates in a 
handle. The thing next in importance is the socket joint of the 
removable pen and pencil parts. 

(b) Tests. All joints in a compass and its parts should work 
in the same plane. To test tbe compass for this, place the parts 
in the socket and bend the legs out at the head, and then bring 
the points together by bending at the lower joints. If the points 
come exactly together the joints are true. This is also a test of 
the alignment of the shank in the socket. 

(c) Setting the Lead. Before attempting to use the compass 
the lead should be sharpened as described in Art. 65 and 
set as follows: Place the pen in the compass and adjust the 
needle so that it projects slightly beyond the nibs of the pea; re- 
move the pen, replace the pencil and adjust the lead so that it is 
slightly shorter than the needle point. 

{(l) Manipulation. In describing a circle the needle point 
and pen or pencil parts should be bent so that they ai'e perpen- 
dicular to the paper. The needle point will then make only a 
sinall hole, and the nibs of the pen will bear equally upon the 
paper, which is a condition that must be fulfilled in order that 
the line may not be ragged. 



Having set the compass approximately and adjusted it exactly 
with the hair-spring thumb screw, grasp the handle between the 
thumb and forefinger and with the needle point resting lightly 
on the center, and the compass leaning a little in the direction 
of motion, start with the lead or pen about under the wrist and 
swing in the circle without stopping. The motion should be in 
a clockwise dii-ection. Let one passing of the lead or pen suffice. 
Do not go over the line again either backward or forward. 

When using the lengthening bar, the length of which makes 
the instrument somewhat unwieldy, the pen or pencil part should 
be steadied by grasping it lightly between the thumb and fore- 
finger of the free hand. 

(e) Care. The compass should be carefully guarded against 
injur^^ Falling on the floor may spoil the alignment. The 
needle point should always be very sharp. When dull it may 
either be sharpened on a fine grained oil stone or replaced by a 
new one. It is a common fault with beginners to clamp the 
points and head joint too tight, with the idea that they will 
remain more securely in place. The joint should work easily. 
If clamped too tight it is difficult to set the points to the required 
distance as they will spring slightly when released. The screws 
should not be set down hard in clamping the points as this 
destroj^s the screw threads. The points will remain securely in 
place with careful handling if clamped lightl3\ 

83. Bow Pen, Bow Pencil and Bow Dividers. The bow 
pen and pencil serve the same purposes as the compass, and the 
bow dividers take the place of the large dividers, in describing 
small circles, and laying off small distances, where the larger 
ones are too heavy and less accurate. They have the advantage 
that they retain their adjustment. 



51 



84. Titles. The relative importance of the various items of 
the title is shown by their arrangement and the character of the 
letters in which they are printed. 

(«) Balancing the Title. A title of two or more lines should 
be arranged so that the middle point of each line is on the same 
vertical straight line. The title is then said to be balanced. To 
balance the title each line should first be lettered on a scrap of 
paper, taking care to make it accurate in height and to space 
the letters correctly. Each line should be complete in itself, but 
it need not have any definite relation to the other lines at this 
stage. Mark the middle point of each line and cut out strips of 
paper containing the lines. Fig 76A. Draw pencil guide lines 
on the sheet according to the layout given. Select the strip 
containing the longest line of the title and lay it above its space 
on the sheet with one end of the line one-half inch from the 
right border line. Fig. 76 B. Mark the middle point on the 
sheet and draw a vertical line through it. This will be the 
center line of the title. The printed lines may now be laid 
above the spaces with their middle points on the center line and 
lettered according to the spacing on the trial slip. 



c.onnk: riNCn Kc^n 



Z2IB: 



^;^x4^"C0K'nSS HNrTWF 



I WAN 1 n) - Ht:^Rr-,Hn stfh 



scAi I- -Tyrn^RThR si7h 



1 





A 


















1 WAMTFn - F 


DHGb.n STht-l ( 


1 WANTH-n - F")RrAFf^ STFFl 1 















B 
Fig. 76 



Make a complete pencil drawing of the figures on page 53 as 
shown. 

85. Penciling". In making dashed lines with the compass 
the lead should be sharpened to a conical point in order that the 
end of the dashes may be made distinct. A vertical and a hori- 
zontal center line should be put through the center of the circles. 
They should extend about Y' beyond the largest circle. All 
dimensions, dimension lines, numerals and letters, except those 
in the title and filing corners of the plate, should be omitted. 

86. Fig'ure 1, Page 53. Locate the center of the figure as 
shown. With the scale and a very sharp pencil, mark off the 
given distance on the radius A. Note. Insert a piece of 



PLATE 3 

"4H lead" in the pencil leg of the compass and bow pencil. 
The leads sold with the instruments are too soft. Draw the 
smallest circle first, drawing the dashed circles as shown. Keep 
the leads sharp. 

87. Fig'ure 2, Page 53. Insert the lengthening bar in the 
compass, and with the center at B describe arcs as shown. Draw 
the filing circle in the lower left hand corner of the sheet, and 
letter therein the appropriate plate number, and filing number. 
Add the initials below the filing circle, keeping the lines of 
figures, and letters symmetrical with reference to an imaginary 
vertical line through the center. 

88. Title. Layout the guide lines for the title in the lower 



52 




53 



right hand corner of the sheet according to the lay out given in 
Fig. 77. 
Letter the following material arranged as given: 

EXERCISES 

WITH 

COMPASS, BOW PENCIL AND BOW PEN 



~^^ 



E 



i 



t 



^^^^: 



Fig. 77 



PLATE 4 

EXERCISES WITH THE COMPASS AND BOW PEN 

89. Make a complete tracing of plate 3. 

Practice with the compass and low pen before inking the re- 
quired plate. 



54 



PLATE S 



SHOP DRAWING IN PENCIL. PLANER CHUCK JAW 
FREEHAND SKETCHING 



90. Materials. The outfit for this course consists of a pencil, 
a pad of cross section paper and a soft eraser- When sketch- 
ing from models a scale, inside and outside calipers and other 
special tools for taking measnremants will also be needed. 
Sketches made from the dimensioned perspective drawings in 
these notes will not require the use of the measuring tools. A 





Fig. 78 A 



Fig. 78 B 



3H pencil is recommended. Cross section paper divided into one- 
eighth inch squares and printed in faint blue lines should be 
used. 

91. StFaig"ht Lines. The pencil should be sharpened to a 
conical point. Sharpen the pencil often. All lines should be 
made freehand, including the circles. The hand should rest on 
its side, the pencil being held nearly perpendicular to the 



line to be drawn. This position makes it possible to draw 
lines from one to two inches long. When longer lines are neces- 
sary they should be made in two or more strokes, each stroke 
beginning at the end of the previous one. Avoid drawing free- 
hand lines by making short overlapping strokes. Each line 
should be drawn faintly at first. If a line is not properly placed 
or its direction is not correct it should be erased and redrawn. 
After all of the views have been completed the lines should be 
gone over, making them distinct. In going over the lines they 
should not be thickened. 

92. Circles. To sketch a circle the horizontal and vertical 
axes are first drawu, as shown in Fig. 78A. Points on the cir- 
cumference are located by estimating the length of the radius 
from the center of the circle. When the circle is small four 
points are sufficient. For larger circles additional lines should 
be drawn at 45° with the horizontal axis and points located on 
them in the same manner. Fig. 78B. The same method may 
be employed for arcs of circles. To sketch an ellipse the ends 
of the major and minor axes should be located. 

93. To Complete Sketch. In making a freehand sketch pro- 
ceed in the following manner. Each step should be completed 
before the next step is considered: 

1. Determine the number and kind of views. The views that 
best represent the object should be selected. 

2- Locate the group of views on the sheet and block out each 
view. See Art. 94. 

3. Draw the center or datum lines. 

4. Complete the views in light lines, proportioning the parts 
by eye. The divisions on the cross section paper should not be 
used as a scale. 



55 



5. Make all lines clear and firm. 

6. Insert dimension and extension lines. 

7. Draw arrowheads. 

8. Put in the dimensions. The arrowheads and numerals 
should be as carefully executed as those on a mechanical drawing. 

9. Section-lining. 

10 Letter the title and add the data in the filing circle. On a 
sketch the height of the letters in each line of the title should 
be the same as for a mechanical drawing. It is not neces- 



sary, however, to balance each line on a vertical center line. An 
example of a title for a sketch is shown in Fig. 79. 



HLANHR CHUCK^TAW- 



1 WAN I l-n-r.ASI IhfTW- 
iJCAL> - HJI I ^\7T^~ 



UNISHFIY 



FiG. 79 



WORKING DRAWINGS 



94. Planning" the Drawing". In deciding the scale of a 
drawing the draftsman must consider not only his convenience 
in drawing the views on the sheet, but also the use to which the 
drawing is to be put. It should not be of such a size as to be 
unwieldly to the mechanic nor small enough to be confusing. 




Fig. 80 

(a) Number, Kind and Arrangement of Vieivs. The number 
of views is determined by what the draftsman's judgment tells 
him makes the drawing thoroughly intelligible to the mechanic. 

All necessary views and no more should be given. Select 
views that show the object in the most comprehensive manner. 
Sectional views often make the inside of an object clearer to the 
mechanic. 



The views must always have a fixed relation to each other ac- 
cording to the rules of third angle projection. 





^ r - ' 




-4 a »- 


i-U c 




TT 


' 1 


1 

r 










r- 

1 

' L _ 




1 



Fig. 81 

(b) Location of Views tvith Reference toEach Other. The dis- 
tance between views of an object should be as small as possible 
and still have each view stand out as a distinct view. For the 
problems of this course the distance between views should as a 
rule be not less than f nor more than l''. 



56 



(c) The Enclosing Rectangle. The rectangle in which the 
views are inscribed is known as the enclosing rectangle. The 
dimensions of the enclosing rectangle are determined for two 
views as follows: Fig. 80, A, the width of the rectangle equals 
a plus b plus e. B, the height of the rectangle equals B. When 
three views are required, Fig. 81, A equals a plus b plus c and 
B equals d plus b plus e. 

In some cases consideration is given to the dimensions to be 




Fig. 82 

placed on the several views in determining the size of the en- 
closing rectangle. In this course the several views are to be 
accurately balanced on the sheet according to the instructions 
here given. 

id) Location of the Dratving Within the Border Line. The 
required group of views is located within the border line by de- 
termining the position of the enclosing rectangle. It should be 
located so that m equals m and n equals n or what is the same 
thing B plus (2 x n) equals W and A plus (2 x m) equals 14", 
Fig. 82. 

95. Working- Methods. From what has already been said 
about speed and accuracy, the need of going about the work 
systematically is easily recognized. The system reduces to what 
is usually termed "drawing by stages." 



(a) Constructive Stage. Under this head comes the laying out 
of the drawing and all instrumental penciling. In this stage all 
lines should be made light and full, no dotted lines being used 
at all. As hard a pencil should be used as the paper will per- 
mit. Lines may be drawn longer than absolutely necessary to 
avoid the possibility of having to patch them. Do not erase 
until the drawing is finished. See page 62. 




Fig. 



(ft) Finishing Stage. Go over all the lines, making them 
heavier and ending them at the proper points. Render all con- 
ventions. Dotted lines may now be made where required, going 
over the light full lines but do not try to erase between the 
dashes. The dashes should be all of the same length and the 
ends well defined. Put in extension and dimension lines, and 
dimensions, also notes and the title. 

96. Conventions, {a) Lines. Fig. 83. A drawing in order 
to be clear and legible must have the different ideas involved 
expressed by characteristic lines. Furthermore it is very essen- 



57 



tial to the good appearance of the drawing that each class of 
lines be uniform in width, density and execution. 

(6) Object Lines. Lines representing visible edges are full 
lines. 

(c) Invisible Lines. Lines representing hidden edges are 
dash lines, the same weight as the object line, dashes i" and 
spaces sV" long. 

(d) Dimension and Extension Lines. Dimension lines indi- 
cate dimensions between certain limits. A full line is used. 
It should be broken at some point, preferably the middle, to 
allow putting in the dimension. In general, arrowheads are 
placed one at each end. 

When a dimension is placed off the view, parallel lines are 
extended from the points between which it is to be shown, and 
the dimension line placed between and at right angles to them. 
They should begin ^V" from the object line of which they are a 
continuation and end \" beyond the arrow head. 

97. Dimensioning". Possibly more here than anywhere in 
the drawing is the draftsman's best judgment called into play. 
It is absolutelj^ necessary to avoid mistakes, and to facilitate the 
work of the mechanic, that the necessary dimensions only be 
given, and those placed in such a way as to make the drawing 
easily I'ead and interpreted. Placing o,f dimensions in obscure 
and unexpected places should be avoided, and wherever possible 
they should be grouped in such a manner that their relation to 
each other is obvious. No doubt the best guide to follow is for 
the draftsman to imagine himself in the mechanic's place and 
consider the operations the object must go through in order to 
become a finished product. With this idea in mind, and a 
working knowledge of shop methods, which every draftsman 
should possess, many of the problems will be readily solved, 
To illustrate, when the machinst drills a hole he sets the point 
of the drill at the center, and hence the hole should be dimen- 
sioned by referring its center to some surface, line or point, 
easilj^ accessible. 



(a) Form. The general form of the dimension includes the 
extension and dimension lines, numeral and arrowheads. 

(&) To Read. All dimensions should read from the lower 
and right hand edges of the drawing. 

(c) Notation. Feet and inches are denoted by the signs ' and 
" respectively, thus 5'-6" (not 5 ft. 6 ins). 

(d) Denomination. Dimensions up to 2' are given in inches 
and all above in feet and inches, thus 23^'', 2'-4''. 

(e) Fractions. Conventional fractions are used having de- 



/Tz 




Fig. 84 

nominators as shown, \, j, i, yV, sV, "irV- Do not use such frac- 
tions as tV. ^V. etc. For very accurate dimensions such as clear- 
ance, special fits, etc., decimals are used and are written thus- 
5" + 0.0.06", 3'' -0.0025". 

(/) Height of Numerals and Fractions. Use plain vertical 
figures VV'liig'l^, the numerals in both the numerator and denom- 
inator of the fraction being each 3^" high, or the same as the 
whole number. Leave a small space between the numerals and 
division line of fraction. This adds greatly to the neat appear- 
ance. 

ig) The Scale of the drawing should be placed under the title 
and written thus. Scale Full Size, Scale Half Size. 

(7i) Arrangement. Do not give the same dimension twice, 
nor leave them so that the workman has any calculating to do. 

Judgment must be exercised in placing dimensions on or off 
the views. In general use the method which insures clearness. 



58 



Wheu dimensions are grouped in parallel lines they should be 
graded from the shortest on the inside to the longest outside, 
Fig. 84. This arrangement avoids crossing the dimension lines 
by the extension lines which is confusing. 



Cross-hatching should be broken to allow space for numerals 
but not for the dimension line, Fig. 84. 



PLATE 

98. Given. The perspective view, and the front view 1 and 
right end view 2 in Orthographic projection, of a Planer Chuck 
Jaw, page 61. 

99. Draw (I) A freehand sketch of the Planer Chuck Jaw 



in]io 



7 -l(D I 

4i t 



C 



^. 



T 

nit 



!S|<S 



Fig. 85 



left end view 
for freehand 



similar to the one shown in Fig. 85, showing the 
instead of the right end view. Read instructions 
sketching. Arts 90-93. 

(2) A mechanical drawing showing front and left end view. 
Scale — Full size. 



100. Use. The sketch represents a Planer Chuck Jaw. The 
chuck is bolted to the bed of the planer and holds the piece to 
be planed as in a vice. The Planer Chuck Jaw may be adjusted 
back and forth to accommodate the various sizes of the pieces to 
be planned. 

101. Analysis of Procedure. 
Lay out the border line. Art. 70. 

Lay out the enclosing rectangle. Art. 94. 

Lay out the views very accurately with the sixteenth scale and 
draw very light lines of indefinite length (be sure they are long 
enough) as shown on page 62. 

Draw over the light lines making clear, firm lines ending them 
at the proper points and dotting hidden lines. 

Select carefully the dimensions that are necessary for the me- 
chanic to have in order to make the piece, and arrange them so 
as to show their relation to each other in the clearest possible 
m inner. All figures should be ^V^ high; those in the fractions 
as well as those in the whole number.- Keep the book open on 
the desk when putting in the figures, following carefully the 
general form together with the order, number and direction of 
strokes for each as given on pages 29-36. 

The division line of the fraction should be in line with the 
dimension line. The figures in numei'ator and denominator 
should not touch the division line. It is a good plan to draw 
the division line first in the fraction. All dimensions should 
read from the lower and right hand edges of the sheet. Arrow- 
heads should be about ■§■" long, the point touching the extension 



59 



line. . They should be very narrow, composed of two slightly Print the plate number in the upper half of the filing circle 

curved lines. and the filing number in the lower half as shown in Fig. 75A. 

The pencil should be sharpened often to secure the best re- Print the initials below the filing circle so that they are balanced 

suits. Use a 3H pencil for all freehand work. The student will on the vertical center line of the filing circle, 

in most cases need to give particular attention to the freehand Print the following note in an open space near the views in 

work in order that it keep pace with the progress made in instru- letters sV' high, 

mental execution. FOR ASSEMBLY SEE DRAWING No. 3526 

Extension line should start sV'^ from the object line and con- 
tinue i beyond the arrowhead. 

102. Title. Read Art. 84. Lay out the guide lines for the 
title as given on page 62. Use the following material in the 
order given: 

PLANER CHUCK JAW 

1 WANTED -CAST IRON— FINISHED 

SCALE— FULL SIZE 



60 







0,|<0 



O 



-I© 

(Vi 








5" 
16 














.1 






















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(O|0O 








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UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE I 



61 



PENCIL LAYOUT — LINES ARE VERV LIGHT 




miS 



'///////^7/^^^^■/A'//. 



W//)i/////////. v///////////\ 



•^//////. 



V^/////////////// 






62 



PLATE 6 



TRACING OF PLATE 5. 



103. Ink on the dull side of the tracing cloth. All object 
lines should be black and -^i" in width. Extension and dimen- 
sion lines ai*e one-half the weight of the object lines or rh's" 
(measured by eye) . When ruling fine lines the pen should be 
frequently cleaned and refilled to secure the best results. 

Freehand work should be practiced on a scrap of tracing cloth 
before attempting the work on the required plate. Sample let- 
ters, figures and arrowheads should be submitted to the instruc- 
tors before making the drawing. 

Inking is the last stage of the drawing and may be itself 
divided into stages. It includes the rendering of dimensions 
and lettering, which should come after the instrumental inking. 
Care should be taken to keep all lines of the same class of a 
uniform width. Particular attention should be given in dotted 
lines to make all dashes the same length, with both ends squai-e 



and the spaces equal. Where lines meet they should run into 
each other, neither falling short nor running over. All corners 
should be perfect. 

Caution — Dotted lines when ruled with the same setting of the 
pen as the object lines often appear heavier than the object line 
due to the frequent starting and stopping of the flow of ink. 
Especially is this true if the pen is very full. In this case the 
width of tho dotted line should be slightly reduced. For methods 
of joining lines, see A and B, Fig. 83. 

Use as few dotted lines as clearness will permit. 

104. Arrowheads are black, about \" long. They must be 
made freehand with a common writing pen. They should be 
very slender, hugging the dimension line closely, the barbs be- 
ing slightly curved, coming in tangent to the dimension line at 
its end. 



63 



Plate 7 



SHOP DRAWING IN PENCIL. 

105. Note. The student's drawing is to be made from the 
small sketch. Fig. 87. The drawing on page 65 is similar to 
the one the student is to make and is given to illustrate con- 
ventions, methods of dimensioning, etc. 




"TURRET LATHE BACK REST" 

Use. This piece and another similar to it form what is 
known as the back rest of a turret lathe. The second pierce is 
inverted and placed so that a 90° V is formed between the two. 
The revolving rod, which is being turned rests in this V, and is 
thus prevented from being pushed out of true by the cutting 
tool. 





Fig. 86 



Fig. 87 



106. Given. The front view 1 and right side view 2 of a 
"Back Rest." 

107. Draw. (1) A freehand sketch as for Plate 5, showing 
the front and left side views. 

(2) A mechanical drawing showing front and left side views. 
Scale — Full size. 



108. Analysis of Procedure. 

Lay out the border line. Art. 70. 

Lay out the enclosing rectangle. Art. 94. 

Lay out the views very accurately with the sixteenth scale, 
and draw very light lines of indefinite length. (Be sure they 
are long enough.) Art. 95. 



64 









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UNIVERSITY OF WISCONSIN 
DEPARTMENT OF DRAWING 









65 



Draw over the light lines making clear, firm lines ending them 
at the proper points and dotting hidden lines. 

Select cai'efnlly the dimensions that are necessary for the me- 
chanic to have in order to make the piece, and arrange them so 
as to show their relation to each other in the clearest possible 
manner. Art. 97. 

Exti'eme care is necessary in all freehand work. All figures 




must be of the same height. Arrowheads should be neat and 
trim. The best results are obtained by making each stroke once 
and once only. Do not get into the habit of working over a 
letter two or three times. It is sure to produce an unpleasing 
effect. 

Refer to pages 29-36 while putting in letters and figures. 

109. Conventions. Angles are dimensioned as shown in 
Fig. 88. The dimension lines are arcs with center at the vertex 
of the angle. 

110. Title. Lay out the guide lines for the title in the lower 



right hand corner of the sheet according to Fig. 89. Work up 
the following material into the same form as given: 

BACK REST 

FOR 

24 TURRET LATHE 

2 WANTED, 1 UPPER, 1 LOWER, UPPER DRAWN 

CAST STEEL— FINISHED 

SCALE— FULL SIZE 

Use the method already given for balancing the title. It will 
insure good results and save time in the end. Art. 84. 



-_i© 



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=-103 ' \ \ ' 



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CI 



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W///?^//)(//////'<i\^y//77777Z///////////////7. 



y^/////;-X^v/ /// ///////////////////\^ 



Fig. 89 

Print the plate number in the upper half of the filing circle 
and the filing number in the lower half. Print the initials below 
the filing circle so that they are balanced on the vertical center 
line of the filing circle. 

In an open space near the views, print the following notes in 
letters -^a" high : 

AS SHOWN PATTERN NO. 1798 U 
REVERSE PATTERN NO. 1798 L 



PLATE 8 

TRACING OF PLATE 7 

111. Read the instructions for inking given in Art. 103. 



66 



PLATE 9 



SHOP DRAWING IN PENCIL. BACK BONNET FOR VALVE 



112. Conventions. («) Center Lines. A center line is 
used to indicate a uatni-al axis of symmetry. A main center 
line is one about which the object or view as a whole is symmet- 
rical, while a secondary center line is an axis of symmetry for 
part only of a view or object. The main center lines should ex- 
tend about i" beyond the outline of the view and the secondary 
center line somewhat less. Every circle has two center lines at 
right angles- 
Center lines may be circular as in the case of a group of holes 
arranged on the circumference of a circle. The center line is 
not quite a complete circle. They may also be radial lines, as 
in the above ease, where the other center lines of the holes are 
radial lines from the center of the circular center line. 

(b) Sectioning. The drawing can often be made much clearer 
and simpler by supposing the object cut by a plane and a por- 
tion removed. One of the chief advantages is the reduction in 
the number of dotted lines which become confusing, when a 
number are necessary. Sections are usually taken by passing a 
plane through an axis of symmetr}^ and parallel to one of the 
planes of projection. If by this process the object is divided 
into two similar parts the drawing is termed a half section. 
When the object is symmetrical it is often better to make a 
combined outside and sectional view, the division usually being 
made at the center line. If the two section planes are taken at 
right angles to each other, cutting to the axis of the object, the 
drawing is termed a quarter section. 

The supposedly cut surface is conventionally represented by 
what is called cross-hatching, which consists of very fine paral- 
lel lines equally spaced and inclined to the horizontal. When 
an object consists of more than one part, adjacent surfaces be- 



longing to the different parts are distinguished by sloping the 
lines to right and left respectively. 

Different metals and materials may be characterized by adopt- 
ing characteristic lines, spacing and inclinations, in the hatch- 
ing. The most common one, cast iron, is represented by a fine 
full line about center line weight inclined at 45° and spaced ac- 
cording to the size of the surface. An average spacing is about 




yq" . The spacing is done entirely by the eye. The student 
should practice on a scrap of paper so as to learn to judge the 
spaces correctly before attempting to work on a drawing. Un- 
less he is very careful he will find the width of spaces changing 
as he proceeds, and in order to overcome that difficulty he 
should keep constantly comparing the one he is drawing with 
the first ones drawn. A common method is to estimate the dis- 
tance, b. Fig. 90, from the ruling edge to the last line drawn, in 
doing which it is necessary to make allowance for the space 
taken up by the pen or pencil, thus introducing another factor 
of error. This may be avoided by holding the pen or pencil in 
position against the ruling edge so that it doesn't quite touch 



67 



he cloth or paper, and judging the space, a, from the last line 
drawn to the point of the pen or pencil. It is a process requir- 
ing considerable care and should not be hurried or slighted in 
any way, the usual penalty for which, coming as it does in the 
finishing stage of the drawing, is a rather troublesome erasui'e 
at least. 

113. Dimensions, {n) Diametral Dimensions. Circles should 
be dimensioned on their diameters when possible, but never on a 
center line. Fig. 91- 




Fig. 91 

When there is not room inside the circle to place the figures 
extension lines may be drawn out from the ends of a diameter 
and the figures placed outside. In case it is deemed advisable 
to place the diameter between parallel lines, as in the case of 
the side view of a cj'linder, note should be made of the fact by 
placing DIA. or D. after the dimension. 

(b) Badii. Where there is room the dimensions should be 
placed between the center and the arc. If for any reason the 
space is cramped, or in case of a cross-hatched surface with a 



rounded corner, the center may be ignored and the dimension 
placed as shown in Fig. 92. The notation R. or RAD. should 
be added. In case of arcs of large radius where the center is 
inaccessible dimension as shown. 

ic)8mall Parts. For various methods of dimensioning small 
parts where there is not room to place the figui-es or arrowheads, 
or both between the extension lines, see Fig. 84. 

id) Drilled, Cored or Tapped Holes. A hole to be drilled, 
cored or tapped is dimensioned conventionally by placing in a 
convenient space near the hole, the figures expi'essing its diame- 
ter followed by the woi-d Drill, Core or Tap and underlined by 
a line which is bent if necessary and terminated by an arrow 
inside the circle. Fig. 101. 




lO R 



Fig. 92 

When holes of the same size ai'e symmetricallj' grouped, upon 
which the same operation is to be performed, they ai'e dimen- 
sioned by what is turned a blanket note such as, Core 8 Holes 
r DIA. Drill 16 Holes V DIA., 8 Holes |'' Tap, 1^' Deep. 

114. Note. The instructor will assign one of the three fol- 
lowing problems for Plate 9. 

115. Conventions. View 1 of the Commutator Clamp Ring 
shown on page 71 is a half section. The arc of a circle drawn 
through the center of the holes in view 2, is a circular center 
line. 



68 



BACK BONNET FOR VALVE 

116. Given. The perspective view of a Back Bonnet for a 
Corliss valve. Fig'. 93. 

117. Draw (1.) A freehand sketch showing the orthographic 
views which represent the object in the clearest manner. Do 
not draw unnecessary views. A half section passing through 
two of the one-inch holes is suggested for one of the views. 

(2) A mechanical drawing showing the same views as the 
sketch. Scale — Half size. 

118. Use. The Back Bonnet is a cover plate, which closes 
the opening at the rear of the valve chamber of a Corliss engine. 

119. Title. Lay out the guide lines for the title in the lower 
right hand corner of the sheet according to the lay out given in 
F\g. 94. 

Letter the following material arranged as given : 

BACK BONNET FOR VALVE 

22 X 42 CORLISS ENGINE 

4 WANTED-CAST-IRON— FINISHED 

SCALE— HALF SIZE 



Print the following note near the views in letters ^o' 
6 HOLES EQUALLY SPACED 



high. 




Fig. 9.3 



A 



^mm^M^zmm^/////. 



=-|tD 



u. 



, \1 , 

vmzzzzzzzzzzk 



-1^ 



"=^^7^/////////////////////. 



'^^^Z^^^^SZZZZ^'^ZZZSZZZZZZZZZ^ZZZZZZ^. 



wzzzzzzzzzzz^ 



Fig. 94 



69 



FACE PLATE FOR LATHE 



120. Given. The perspective view of a Face Plate for a 
lathe. Fig. 95. 

121. Draw. (1.) A freehand sketch showing the ortho- 
graphic views which represent the form of the object in the 




clearest manner. Do not show unnecessary views. Usually the 
best views are those involving the least number of hidden edges. 
(2) A mechanical drawing showing the same views as the 
sketch. Scale — Full size. 

122. Use. The Face Plate is screwed to the spindle of the 
lathe as a nut on a bolt. The piece to be turned in the lathe is 
bolted to its flat face. 

123. Title. Lay out the guide lines for the title in the lower 
right hand corner of the sheet according to the layout given on 
page 75. 

Letter the following material as given : 

FACE PLATE 

FOR 

ENGINE LATHE 

1 WANTED— CAST-IRON-FINISHED 

SCALE— FULL SIZE 

Print the following note near the views in letters -i^" high. 
FOR HEAD STOCK AND SPINDLE DETAILS SEE DWGS 
NO. 3958 AND 3959. 



70 




•zzzzaz. 




© © 

FINISH ALU OVER 



\?. HOLES EQUALLY SPACED 



© 



UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE I 



71 



FLANGED BEARING 



I 1 



CD 




124. Given. The perspective view of a Flanged Bearings 
Fig. 96. 

125. Draw. (1) A freehand sketch showing the ortho- 
graphic views which best represent the object. Do not show 
unnecessary views. 

(2.) A mechanical drawing showing the same views as the 
sketch. 

126. This bearing is made in various sizes to suit the size of 
the shaft on which it is to fit. Select the dimensions from the 
table for the shaft, which will make the drawing of a convenient 
size, but dimension the drawing with the symbols. Leave a 
space on the sheet in which to print the table as given. The 
bolt holes should be about -jV'' larger than diameter of the bolt 
to allow for the clearance. 

127. Title. Letter the following words -//' high in the lower 
right hand corner of the sheet. 

FLANGED BEARINGS 



Fig. 96 











DIMENSIONS IN INCHES 

In Orderinfi' Specify Paltem Number. 














Finished 


Rough 




CO 

1 


Pat- 


^ 


A 


B 


c 


T 


A 

3 

31 
H 


B 

1 
3| 


C 


T 

1 

2 


D 

3i 


E 

4 

41 

6,^ 


G 

3J 
4 

41 

5| 


O 

3 
Zl 

4 

il 
5 


H 

i 

ft 


No. 


11 

1 t' V 


4 
4 
4 
4 
4 


1 

2 
i 
i 


R3500 
R3501 


1/s 


si" 

6 


3| 


"i' 


1 1 

16 


R3502 
R3503 


Hi- 










R3504 













II 



72 



128. The work of hiking may be divided into steps as fol- 
lows, beginning at the upper left hand corner and working down- 
ward and to the right: (1) Draw all circles and arcs, the 
smaller ones first and all of the same radius at one setting of 
the compass. (2) Ink vertical lines. (3) Ink all horizontal 



PLATE 10 

TRACING OF PLATE 9 

and other straight lines. (4) Render the dimensions. (5) Put 
in screw thread conventions, show breaks and cross hatch sec- 
tions. (6) Put in the title and ink the border line. 

129. Center lines are full black lines and about i the weight 
of the object line or j^-g in. in width. 



PLATE 11 



SHOP DRAWING IN PENCIL. 

130. Conventions. View 1 of the gland shown on page 76, 
illustrates the quarter section. Read Art. 112b. 

Especial attention is called to the fact that there is an object 
line across the middle of the section view representing the edge 
of the lower half of the object, which is the result of the hori- 
zontal cut. 

Note the method of dimensioning the arc of |" radius on 
sheet. 

To insure accuracy points of tangency are located exactly by 
the method illustrated in Fig. 97. A triangle a is placed with 
its edge along the tangent line as shown in dotted lines, a sec- 
ond triangle b is placed against the first and held stationary 
while the first is revolved into the second position in which one 
edge is perpendicular to the tangent line and passes through the 
center of the ai-c. According to the laws of geometry the foot 
of the radius perpendicular to the tangent line is the point' of 
tangency. The point of tangency should be located by a short 
mark as shown at c. The lines marking the points a of tan- 



"STUFFING BOX GLAND" 

gency should be left as a guide in inking but should not be 
traced. 




131. 

Fig. 98 



Given. 



Fig. 97 
The perspective view of a Stuffing Box Gland. 



73 



132. Draw (1.) A freehand sketch showing the ortho- 
graphic views which will best represent the object. It is sug- 
gested that one of the views be a quarter section view. 




Fig. 



(2.) A mechanical drawing from the sketch. Scale — Full 
size. 

133. Use. The gland is the piece which fits around the pis- 
ton or valve rod, and when forced into the stuffing box, com- 
presses the packing thus forcing the packing against the rod and 
making a steam tight joint as the rod moves into and out of the 
cylinder or steam chest. 

134. Analysis of Procedure. The original pencil layout 
for this sheet will look like that on page 75, that is all lines in- 
cluding the circular arcs are drawn longer. than necessary and 
are as light as possible. The ares are drawn first and the tan- 
gent lines drawn by placing a straight edge so that a line ruled 
along it will just touch the ares. 

135. Title. Use the layout for the title on page 75 and the 
material given below. 

GLAND 

FOR 

THROTTLE VALVE STUFFING BOX 

1 WANTED -CAST-IRON— FINISHED 

SCALE— FULL SIZE 

Fill in the filing circle as usual. 



PLATE 12 

TRACING OF PLATE II 

136. Read carefully Art. 128. It is essential that the ares be 
drawn first, stopping them exactly at the points of tangency to 
insure good joints. The points of tangency should be located 
in pencil on the tracing cloth. Art. 130. 



74 






I Ma 



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75 




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FINISH AUU OVER 



209 




UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE I 



76 



PLATE 13 



SHOP DRAWING IN PENCIL. BRACKET 

137. Conventions. {!) Screw Threads are h&sed on the cuwe of a right square thread whei*e the cui'ves are replaced by 

"which is known as the helix. Fig. 99 A. It is generated by a straight lines. 

point which moves on the surface of a cylinder with a uniform V Thread. Fig. 100 A, is the projection of a V thread. B 

motion parallel to the axis and at tlie same time rotates about and C, Fig. 100, are conventional representions of the V thread. 





the axis with a uniform motion. The distance traversed by a 
point pai-allel to the axis in one revolution is called the pitch. 
In the case of threads this is the distance measured parallel to 
the axis between corresponding points on two successive threads. 
Square Thread. Fig. 99 B, shows the projection of a right 
square thread. Fig. 99 C, shows the conventional representation 



B is sometimes used when the drawing is made to large scale or 
for exhibition purposes, but C is used in common practice. C 
is arrived at by first making the curved lines straight and then 
omitting the short lines forming the saw edge. 

Methods of representing the side, section and end views of 
tapped holes and bolts are shown at B and C, Fig. 101. These 



77 




threads at the left (sectional portion), are imperfect at the top 
and root, the next two are imperfect at the top only, and all to 
the right of these are full threads. 



ABC 

Fig. 101 

should be carefully studied and kept in mind for future use. 
Note that the inclination of the threads in the section of the 
tapped hole is opposite to that of the bolt which fits it. 

The Pipe Thread is illustrated in Fig. 102. In order to insure 
tight joints the threaded portion tapers as shown. The first four 



TAPER \ IN 32 





Fig. 103 



V? 



\t:iA 



^ 



r o 
I ly 

iJlt 



^ 



Q 



Eg 



ikd 



2D 
B 



Fig. 102 



Bolts. Fig. 103 A and B, give the proportions for drawing 
hexagonal head and square head bolts. These proportions do 
not coiTespond to the actual dimensions. See a table of bolt 
and nut sizes for actual sizes. 



78 



A Stud. Fig. 104 A, is a rod of metal threaded at both 
ends, and is used for fastening on such things as cylinder heads. 
The figure illustrates the method of its application. 

A Cap Screw. Fig. 104 B is a rod of metal with a head at 





one end and threaded at the other for about two-thirds of its 
length. 

Machine screws are similar to cap screws, and are used for 
like purposes, but usually for smaller work. The main point of 
diiference is that cap screws are measured in inches, while ma- 



chine screws are designated by a machine screw gage. Both have 
heads of various shapes. 

Set Screw. Fig. 104 C shows a set screw. Its function is 
to prevent relative motion of the two parts which are held in 
contact by some other means, as, for instance, a shaft in the 
hub of a pulley. 

138. Centers for rounded corners, fillets and other arcs which 
do not have their centers on any line of the drawing are located 



...ih ^ 


a 


^_^ 


c 







Fig. 105 

by what is called the "trial and error" method. First adjust 
the compass to the proper radius, then set the lead on the tan- 
gent line at a. Fig. 105, making ac as nearly as possibly equal 
to the radius (by eye). Set the needle point opposite a and 
bring the lead around to d. Move the needle point parallel to 
ae an amount equal to the error. 

139. Broken Lines. Where it is desired to show a broken 
edge a ragged line is drawn, with a writing pen, of about the 
same weight as the object line. 



PLATE 13 



140. Given. The front view, 1, the end view, 2, section on 
AA, 3, and the true outline of the flanges 4. Fig. 107. 

141. Draw (1.) A freehand sketch showing a shop solu- 
tion, i. e., a solution in which the plotting of points is avoided 
by the use of auxiliary views. 



(2.) A mechanical drawing from the sketch. Scale — Full 
size. 

142. Use. The bracket is that part of a drill grinder which 
serves to support the V shaped holder into which the drill is 
placed for grinding. The cylindrical part whose axis is hori- 



79 



zontal fits over and is clamped to a cylindrical projection from the 
frame of the machine. A cylindrical projection on the tool 
holder mentioned above fits into the inclined hole and is clamped 




Fig. 106 

just tight enough so that it may turn without jarring when the 
machine is in operation. 

143. Dimensioning". The arrangement of dimensions on 
the sketch given is not the best, and in view of the fact that ad- 



ditional or different views are necessary in the solution, the stu- 
dent will need to exercise his judgment in the disposition of 
dimensions so as to make the drawing read as clearly and easily 
as possible. 



SECTION ON AA. 



OUTLlMt OF *LANGes 




Fig. 107 

As far as possible the dimensions for the section should be 
placed on the section rather than on the other views. 

The i" hole in the web which joins the two cylindi"ical parts 
should be marked "core" as it is made by a core of sand in 
casting. 



80 



The Y' slots should be cut with a i" milling cutter and note 
should be made to that effect in connection with the dimension. 

The surface on which the heads of the studs will rest should 
be finished, and as it is only necessary to finish these spots, the 
operation should be noted by marking them "spot face." 

In the solution of this problem it will be necessaiy to give 
some partial views, i. e., views which only show part of the ob- 
ject. In a case of this kind where it is necessary to consider 
part of the object broken away, a ragged line is drawn, with the 
writing pen, across where the break occurs. 

When a section of some part of the object is shown in a sepa- 
rate view, a line should be drawn where the plane of the section 
cuts the object and labeled, as for instance, A A, a note being 
made near the section view "section on AA." 



All of the surfaces of this object are not to be finished and 
consequently the word "finished' must be omitted from the 
title. Those surfaces which are to be finished are marked in 
the view where they show as a line with an /as in Fig. 107, or 
the finish is indicated in some other way, such as by print- 
ing the word "bore," "turn," etc., with the dimension on a 
diameter. 

144. Title. Use the title layout given on page 75 and the 
material given below. 

DRILL REST BRACKET 

FOR 

YANKEE DRILL GRINDER 

1 WANTED CAST IRON 

SCALE FULL SIZE 



PLATE 14 

TRACING OF PLATE 13 



81 




^."■^ ^ 3 



SECTION AA 

® 



SECTION BB 

® 





UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE t 



82 



PLATE \S 

SHOP DRAWING IN PBNCIL.— "CHECK WASHER" 



145. Given. The front view 1, and auxiliary view 2. Fig. 
108. 

146. Draw. The front, auxiliary and top views. Scale — 
Full size. 

147. Use. A washer of this kind is used in wooden roof 
trusses. Its function is to furnish a fiat bearing for the head of 
a bolt which passes obliquely through a timber. The lugs on the 
under side are let into the wood to prevent it from sliding. 

148. Title. Use the layout given for Plate 11. 

CHECK WASHER 

FOR 

WOODEN ROOF TRUSS 

24 WANTED -CAST-IRON 

SCALE— FULL SIZE 




Fig. 108 



PLATE 16 

TRACING OF PLATE 15 




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UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE 2 



84 



CHAPTER 4 



ISOMETRIC AND CABINET PROJECTION 



149. Isometric Projection is a method of representing- an 
object in one view. This view shows more than one face of an 
object thus giving the effect of a picture. Because the theory 
involved is much simpler and its application is much easier this 
method is often preferable to the exact pictorial representation 
afforded by perspective. An isometric drawing of an object is 





Fig. 109 

usually termed the "isometric" of the object. Isometric is used 
for illustrating parts of machines or structures where the ortho- 
graphic is hard to read, or for those who are unaccustomed to 
reading working drawings. It is also used in patent office 
drawing. 

150. Derivation of Axes. If a cube is placed so that one 
of its diagonals is perpendicular to a plane of projection, the 
projection of the cube upon the plane will appear as in Fig. 



109 A. The projections of the three nearest edges of the cube 
a b, b C and b d make equal angles with each other ( 120°) . 

Under the conditions stated the edges of the cube all make 
the same angle, with the plane of projection. There projections 
are, therefore, all foreshortened in the same ratio. This fore- 
shortening is generally disregarded, and the lines made actual 
lengths in the drawing. The only effect of this is to change the 
scale of the drawing. 




Fig. 110 

It has been stated that the cube was placed with a diagonal 
perpendicular to the plane of projection. Its position is further 
limited by turning it about this diagonal until the projections of 
two of the near edges make 30° with a horizontal line, while the 
third is vertical. Fig. 109 B. These three lines represent the 
dimensions of the cube, and consequently its isometric may be 
drawn by laying off lengths pai-allel to these lines. They are 
called the isometric axes. 



The following is a summary of the underlying principles of 
isometric drawing. 

(a) The axes represent three lines mutually at right angles, 
thus corresponding in length, breadth and height. All measure- 
ments on the drawing must he laid off parallel to these axes. 




Fig. Ill 

(&) Parallel lines in the object are parallel in the draiving. 
Vertical lines are drawn vertical. 
151. Non-isometrie Lines. Lines of the object which 



X 










a 
\b 


9 







1 




y 




Fig. 112 



cannot be drawn parallel to one of the three axes are termed 
non-isometric lines. Such lines must be drawn by co-ordinates 
taken parallel to the axes as shown in Fig. 110. 



(a) The work of laying out non-rectangular plane figures 
maybe simplified if they can be inscribed in rectangles. Fig. 111., 




Fig. 113 

(b) Three dimension figures may be laid out in a manner sim- 
ilar to that shown for plane figures by introducing a third co- 
ordinate. Fig. 112. 





Fig. 114 

(c) Non-rectangular solids which can be inscribed in a rectan- 
gular prism may be drawn as in Fig. 11-3. 

152. Approximate Isometric Circles. Circles may be 
drawn more easily, though not so accurately, by the following 
method. Draw first the isometric of the square circumscribing 



86 



the circle. The center d, Fig. 114, for the short radius r is found 
by striking an arc with center at a and radius ac = i ab, P=de. 
The center of the long radius R is located by striking an arc 
with its center at C with radius = ab, R = ec = ab. 

153. Cabinet Projection. The uses and fundamental prin- 
ciples are very similar to Isometric Projection. Fig. 115. Here 
one face of the object is parallel to the plane of projection. 
There are three axes, one horizontal, one vertical and one at 45°. 
Actual lengths are laid off parallel to the horizontal and vertical 
axes. One-half actual lengths are laid out parallel to the 45° 
axis- Circles in planes parallel to the plane of projection show 
as true circles. All others must be plotted. 



Fig. 115 



Plate 17 



154. Made an isometric and a cabinet drawing of the pyra- 
mid described in the following problem. Place the top and front 
views in the middle of the sheet in orthographic projection. To 
the right of this draw the cabinet and to the left the isometric. 
Ink in the drawing on the paper. 

155. Title. Beneath each view print the name correspond- 
ing: Isometric, Orthographic and Cabinet in vertical capi- 
tals i^" high. 



156. Draw. A hexagonal pyramid 82'' high; side of hexag- 
onal base li" long. Half way up the sides of the pyramid is a 
groove extending entirely around the pyramid. This groove is 
formed by removing the portion of the pyramid between two 
cuts, each |" deep (measured parallel to the plane of the cut and 
perpendicular to the edge of the hexagon). The planes of both 
cuts are parallel to the planes of the base of the pyramid. The 
perpendicular distance between the planes of the two cuts is \" . 
(From Tracy's Mechanical Drawing.) 



87 



SEP 28 WJ5^ 



PLATE 18 



157. Make a working drawing of a wooden box. Scale — 




Fig. 116 



Half size. The top of the box is 10" x 16'' OA (over all), 
bottom 8i x 12^-' ' OA; depth 3" OA. Opposite sides have the 



same slope. The bottom board laps over the sides and the sides 
lap over the ends. Thickness of material i". A vertical par- 
tition which is parallel to the longer edges divides the box into 
two equal compartments. The upper part of this partition is 
cut into the form of a handle as shown in Fig. 116- Show all 
dimensions. Ink on paper. 

A note should be printed on the drawing in inclined lower 
case letters as follows, — Hard wood — all joints glued and nailed 
— thickness of material i". 

158. Title. 

TOOL TRAY 
SCALE— HALF SIZE 



PLATE 19 

159. Make an isometric of the box in Plate 18. Copy the 
note and title. Show all dimensions. Ink on paper. 



88 



